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R/qmleLevy.R
In yuima: The YUIMA Project Package for SDEs
Defines functions
qmleLevy
Documented in
qmleLevy
########################################################################
# Stepwise estimation for ergodic Levy driven SDE
########################################################################
#qmleLevy<-function(yuima,start,lower,upper,joint = FALSE,third = FALSE,
# Est.Incr = c("NoIncr","Incr","IncrPar"),
# aggregation = TRUE)
qmleLevy<-function(yuima,start,lower,upper,joint = FALSE,third = FALSE,
Est.Incr = "NoIncr",
aggregation = TRUE)
{
oldyuima<-yuima #line1
myjumpname <- yuima@model@jump.variable
mymeasureparam <- yuima@model@parameter@measure
if(!(Est.Incr %in% c("NoIncr","Incr","IncrPar")))
stop("Argument'Est.Incr' must be one of \"NoIncr\",\"Incr\" or \"IncrPar\"")
call <- match.call()
truestart<-start
cat("\nStarting QGMLE for SDE ... \n")
parameter<-yuima@model@parameter@all
orig.mylaw<-yuima@model@measure
mylaw<-yuima@model@measure$df
numbLev<-length(yuima@model@measure.type)
if(missing(yuima))
yuima.stop("yuima object is missing.")
if(!is(yuima,"yuima"))
yuima.stop("This function is for yuima-class.")
if(length(yuima@model@parameter@jump)>0)
paracoef <- yuima@model@parameter@jump
if(length(yuima@model@parameter@drift)>0)
paracoef <- c(paracoef, yuima@model@parameter@drift)
if(Est.Incr == "IncrPar"){
start0<-start
lower0<-lower
upper0<-upper
lev.names<-yuima@model@parameter@measure
}
DRIFT <- yuima@model@drift
JUMP <- yuima@model@jump.coeff
sdeModel<-yuima@model
if(length(sdeModel@parameter@measure)!=0){
nPar<-length(sdeModel@parameter@measure)
for(i in c(1:nPar)){
assign(x = sdeModel@parameter@measure[i],
value = start[[sdeModel@parameter@measure[i]]])
}
names1 <- names(start)
index <- which(names1 %in% sdeModel@parameter@measure)
start <- start[-index]
names1 <- names(lower)
index <- which(names1 %in% sdeModel@parameter@measure)
lower <- lower[-index]
names1 <- names(upper)
index <- which(names1 %in% sdeModel@parameter@measure)
upper <- upper[-index]
}
#if(class(sdeModel@measure$df)!="yuima.law"){
if(!inherits(sdeModel@measure$df, "yuima.law")){ # fixed by YK
code <- suppressWarnings(sub("^(.+?)\\(.+", "\\1", sdeModel@measure$df$expr, perl=TRUE))
candinoise<-c("rNIG","rvgamma","rnts","rbgamma")
if(is.na(match(code,candinoise))){
yuima.stop("This function works only for the standardized normal inverse Gaussian process, variance gamma process, bilateral gamma process, and normal tempered stable process now.")
}
if(length(sdeModel@xinit) == 1){
args <- unlist(strsplit(suppressWarnings(sub("^.+?\\((.+)\\)", "\\1", sdeModel@measure$df$expr, perl=TRUE)), ","))
if(code == "rNIG"){
if(!((abs(eval(parse(text = paste("(",args[5] ,")+(", args[3], ")*(", args[4],
")/sqrt((", args[2], ")^2-(", args[3], ")^2)" )))) < 10^(-10))
&& (abs(eval(parse(text = paste("(",args[2], ")^2*(", args[4], ")/(sqrt((", args[2],
")^2-(", args[3], ")^2))^3"))) -1) < 10^(-10))))
{
yuima.stop("This function is only for standardized Levy noises.")
}
}
else if(code == "rvgamma"){
if(!((abs(eval(parse(text = paste("(", args[5], ")+2*(", args[2], ")*(", args[4], ")/((", args[3], ")^2-("
, args[4], ")^2)" )))) < 10^(-10))
&& (abs(eval(parse(text = paste("2*((", args[2], ")*(", args[3], ")^2+(", args[4], ")^2)", "/(("
, args[3], ")^2-(", args[4], ")^2)^2"))) - 1) < 10^(-10))))
{
yuima.stop("This function is only for standardized Levy noises")
}
}
else if((code == "rnts")){
if(!((abs(eval(parse(text = paste("(", args[6], ")-(", args[2], ")*(",
args[3], ")*(", args[4], ")^((", args[2],
")-1)*gamma(1-(", args[2], "))*(-1/(", args[2],"))*(", args[5],
")"
)))) < 10^(-10))
&&(abs(eval(parse(text = paste("(", args[3], ")*(", args[2],")*((", args[2], ")-1)*gamma(1-(", args[2], "))*(-1/(", args[2],"))*(", args[4], ")^((",args[2], ")-2)*(", args[5], ")^2-(",
args[2], ")*(", args[3], ")*(", args[4], ")^((", args[2], ")-1)*gamma(1-(", args[2], "))*(-1/(", args[2],"))"
))) - 1) < 10^(-10))))
{
yuima.stop("This function is only for standardized Levy processes.")
}
}else if(code == "rbgamma"){
if(!((abs(eval(parse(text = paste("(", args[2], ")/(", args[3],")-(", args[4],")/(", args[5], ")")))) < 10^(-10))
&& (abs(eval(parse(text = paste("(", args[2], ")/(", args[3], ")^2","+(", args[4],")/(", args[5],")^2"
))) - 1) < 10^(-10) )))
{
yuima.stop("This function is only for standardized Levy processes.")
}
}
}else{
warning("In this version, the standardized conditions on multidimensional noises can not be verified.
The expressions of mean and variance are given in help page.")
# The noise condition checker below does not work now (YU: 3/23).
# args <- suppressWarnings(sub("^.+?\\((.+)\\)", "\\1", sdeModel@measure$df$expr, perl=TRUE))
# yuimaEnv <- new.env()
# yuimaEnv$mean <- switch(code,
# rNIG = function(x=1,alpha,beta,delta0,mu,Lambda){mu+as.vector(delta0/(sqrt(alpha^2-t(beta)%*%Lambda%*%beta)))*Lambda%*%beta},
# rnts = function(x=1,alpha,a,b,beta,mu,Lambda){mu+gamma(1-alpha)*a*b^(alpha-1)*Lambda%*%beta},
# rvgamma = function(x=1,lambda,alpha,beta,mu,Lambda){mu+as.vector(2*lambda/(alpha^2-t(beta)%*%Lambda%*%beta)^2)*beta}
# )
#
# yuimaEnv$covariance <- switch(code,
# rNIG = function(x=1,alpha,beta,delta0,mu,Lambda){as.vector(delta0/(sqrt(alpha^2-t(beta)%*%Lambda%*%beta))^3)*Lambda%*%beta%*%t(beta)%*%Lambda+as.vector(delta0/sqrt(alpha^2-t(beta)%*%Lambda%*%beta))*Lambda},
# rnts = function(x=1,alpha,a,b,beta,mu,Lambda){a*(1-alpha)*gamma(1-alpha)*b^(alpha-2)*Lambda%*%beta%*%t(beta)%*%Lambda+a*gamma(1-alpha)*b^(alpha-1)*Lambda},
# rvgamma = function(x=1,lambda,alpha,beta,mu,Lambda){as.vector(4*lambda/(alpha^2-t(beta)%*%Lambda%*%beta)^2)*Lambda%*%beta%*%t(beta)%*%Lambda+as.vector(2*lambda/alpha^2-t(beta)%*%Lambda%*%beta)*Lambda}
# )
# judgemean<-sum(eval(parse(text = paste("mean","(",args,")")),yuimaEnv)==numeric(length(sdeModel@xinit)))
# judgecovariance<-sum(eval(eval(parse(text = paste("covariance","(",args,")")),yuimaEnv)==diag(1,length(sdeModel@xinit))))
# if(!((judgemean==length(sdeModel@xinit))&&(judgecovariance==length(sdeModel@xinit)*length(sdeModel@xinit))))
# {
# yuima.stop("This function is only for standardized Levy processes.")
# }
}
}else{fullcoef<-NULL}
yuima@sampling@delta <- yuima@sampling@delta[1]
yuima@model@noise.number <- as.integer(yuima@model@equation.number)
if(!joint){
DRIFT <- yuima@model@drift
DRPAR <- yuima@model@parameter@drift
if(length(yuima@model@parameter@jump)>0)
fullcoef <- yuima@model@parameter@jump
if(length(DRPAR)>0)
fullcoef <- c(fullcoef, DRPAR)
oo <- match(yuima@model@parameter@all, fullcoef)
yuima@model@parameter@all <- yuima@model@parameter@all[order(oo)]
oo <- match(names(start), fullcoef)
start <- start[order(oo)]
oo <- match(names(upper), fullcoef)
upper <- upper[order(oo)]
oo <- match(names(lower), fullcoef)
lower <- lower[order(oo)]
yuima@model@diffusion <- yuima@model@jump.coeff
yuima@model@parameter@diffusion <- yuima@model@parameter@jump[1:length(yuima@model@parameter@jump)]
yuima@model@parameter@all <- yuima@model@parameter@diffusion
for(i in 1:length(yuima@model@drift)){
yuima@model@drift[i] <- expression((0))
}
yuima@model@jump.coeff <- list()
yuima@model@parameter@drift <- character(0)
yuima@model@measure <- list()
yuima@model@jump.variable <- character(0)
yuima@model@measure.type <- character(0)
yuima@model@parameter@jump <- character(0)
yuima@model@parameter@measure <- character(0)
diffstart <- start[1:length(yuima@model@parameter@diffusion)]
diffupper <- upper[1:length(yuima@model@parameter@diffusion)]
difflower <- lower[1:length(yuima@model@parameter@diffusion)]
fres <- qmle(yuima=yuima,start=diffstart,lower=difflower,upper=diffupper,rcpp = TRUE,joint = FALSE,method = "L-BFGS-B")
DiffHessian<- fres@details$hessian #182
DIPAR <- yuima@model@parameter@diffusion
DIFFUSION <- yuima@model@diffusion
yuima@model@parameter@all <- DRPAR
yuima@model@parameter@drift <- DRPAR
yuima@model@drift <- DRIFT
dristart <- start[-(1:length(yuima@model@parameter@diffusion))]
driupper <- upper[-(1:length(yuima@model@parameter@diffusion))]
drilower <- lower[-(1:length(yuima@model@parameter@diffusion))]
partcoef <- yuima@model@parameter@diffusion
ov <- match(yuima@model@parameter@drift,partcoef)
ovp <- which(!is.na(ov))
if(length(ovp)>0)
{yuima@model@parameter@drift <- yuima@model@parameter@drift[-ovp]}
yuima@model@parameter@all <- yuima@model@parameter@drift
ma <- match(names(fres@coef),partcoef)
sort <- fres@coef[order(ma)]
esti <- numeric(length(partcoef))
newdiff <- yuima@model@diffusion
newdri <- yuima@model@drift
for(i in 1:length(partcoef))
{
esti[i] <- as.character(fres@coef[[i]])
}
if(length(yuima@model@drift) == 1){
for(i in 1:length(partcoef))
{
newdri <- gsub(partcoef[i],esti[i],newdri)
yuima@model@drift[1] <- parse(text = newdri[1])
newdiff[[1]] <- gsub(partcoef[i],esti[i],newdiff[[1]])
yuima@model@diffusion[[1]] <- parse(text = newdiff[[1]])
}
}else{
for(i in 1:length(partcoef))
{
for(j in 1:length(yuima@model@drift))
{
newdri[j] <- gsub(partcoef[i],esti[i],newdri[j])
yuima@model@drift[j] <- parse(text = newdri[j])
}
for(k in 1:length(yuima@model@diffusion)){
for(l in 1:length(yuima@model@diffusion[[1]])){
newdiff[[k]][l] <- gsub(partcoef[i],esti[i],newdiff[[k]][l])
yuima@model@diffusion[[k]][l] <- parse(text = newdiff[[k]][l])
}
}
}
}
yuima@model@parameter@diffusion <- character(0)
sres<-qmle(yuima=yuima,start=dristart,lower=drilower,upper=driupper,rcpp = TRUE,method = "L-BFGS-B")
DriftHessian <- sres@details$hessian #239
if((length(ovp) == 0) && (third)){
yuima@model@diffusion <- DIFFUSION
yuima@model@drift <- DRIFT
yuima@model@parameter@diffusion <- DIPAR
yuima@model@parameter@all <- DIPAR
newdri <- yuima@model@drift
for(i in 1:length(sres@coef))
{
esti[i] <- as.character(sres@coef[[i]])
}
if(length(yuima@model@drift)==1){
for(i in 1:length(sres@coef))
{
newdri <- gsub(yuima@model@parameter@drift[i],esti[i],newdri)
yuima@model@drift[1] <- parse(text=newdri[1])
}
}else{
for(i in 1:length(sres@coef))
{
for(j in 1:length(yuima@model@drift))
{
newdri[j] <- gsub(yuima@model@parameter@drift[i],esti[i],newdri[j])
yuima@model@drift[j] <- parse(text = newdri[j])
}
}
}
yuima@model@parameter@drift <- character(0)
too <- match(names(fres@coef),names(diffstart))
diffstart <- diffstart[order(too)]
for(i in 1:length(diffstart)){
diffstart[[i]] <- fres@coef[[i]]
}
tres <- qmle(yuima=yuima,start=diffstart,lower=difflower,upper=diffupper,rcpp = TRUE,joint = FALSE,method = "L-BFGS-B")
res <- list(first = fres@coef, second = sres@coef, third = tres@coef)
}else if((length(ovp) > 0) || !(third)){
coef<-c(sres@coef,fres@coef)
mycoef<-unlist(truestart)
#mycoef1<-mycoef[names(coef)]
mycoef2<-mycoef[!names(mycoef)%in%names(coef)]
mycoef<-c(coef,mycoef2)
vcov0<-matrix(NA,nrow = length(coef),ncol=length(coef))
rownames(vcov0)<-names(coef)
colnames(vcov0)<-names(coef)
min0<- c(fres@min,sres@min)
details0<-list(sres@details,fres@details)
nobs0<-sres@nobs
res<-new("yuima.qmle", call = call, coef = coef, fullcoef = mycoef,
vcov = vcov0, min = min0, details = details0, minuslogl = minusquasilogl,
method = sres@method, nobs=nobs0, model=sdeModel)
# res <- list(first = fres@coef, second = sres@coef)}
if(length(oldyuima@data@zoo.data)==1){
myGamhat <- matrix(0,length(coef),length(coef))
myGamhat[1:dim(DiffHessian)[1],1:dim(DiffHessian)[2]]<-DiffHessian
myGamhat[dim(DiffHessian)[1]+1:dim(DriftHessian)[1],dim(DiffHessian)[1]+1:dim(DriftHessian)[2]]<-DriftHessian#293
myGamhat<-myGamhat/oldyuima@sampling@Terminal
}else{
myGamhat <- matrix(0,length(coef),length(coef))
myGamhat[1:dim(DiffHessian)[1],1:dim(DiffHessian)[2]]<-DiffHessian*oldyuima@sampling@Terminal/oldyuima@sampling@n
myGamhat[dim(DiffHessian)[1]+1:dim(DriftHessian)[1],dim(DiffHessian)[1]+1:dim(DriftHessian)[2]]<-DriftHessian#293
myGamhat<-myGamhat/oldyuima@sampling@Terminal
}
}else{
yuima.stop("third estimation may be theoretical invalid under the presence of an overlapping parameter.")
}
}else{
if(third){
yuima.stop("third estimation does not make sense in joint estimation.")
}
if(length(yuima@model@parameter@jump)>0)
fullcoef <- yuima@model@parameter@jump
if(length(yuima@model@parameter@drift)>0)
fullcoef <- c(fullcoef, yuima@model@parameter@drift)
oo <- match(yuima@model@parameter@all, fullcoef)
yuima@model@parameter@all <- yuima@model@parameter@all[order(oo)]
yuima@model@parameter@all <- yuima@model@parameter@all[1:length(which(!is.na(oo)))]
yuima@model@diffusion <- yuima@model@jump.coeff
yuima@model@jump.coeff <- list()
yuima@model@parameter@diffusion <- yuima@model@parameter@jump[1:length(yuima@model@parameter@jump)]
yuima@model@measure <- list()
yuima@model@jump.variable <- character(0)
yuima@model@measure.type <- character(0)
yuima@model@parameter@jump <- character(0)
yuima@model@parameter@measure <- character(0)
# jres<-qmle(yuima,start = start,lower = lower,upper = upper,rcpp = TRUE, joint = TRUE,method = "L-BFGS-B")
# res<-list(joint = jres@coef)
res<-qmle(yuima,start = start,lower = lower,upper = upper,rcpp = TRUE, joint = TRUE,
method = "L-BFGS-B")
}
if(Est.Incr == "NoIncr"){
return(res)
}
cat("\nStarting Estimation of Levy Increments ... \n")
data <- get.zoo.data(yuima)
s.size<-yuima@sampling@n
if(length(data)==1){
X<-as.numeric(data[[1]])
pX<-X[1:(s.size-1)]
inc<-double(s.size-1)
inc<-X[2:(s.size)]-pX
}else{
pX<- simplify2array(lapply(X = data,
FUN = as.numeric))
pX<-pX[-nrow(pX),]
inc<- simplify2array(lapply(X = data,
FUN = function(X){diff(as.numeric(X))}))
}
modeltime<-yuima@model@time.variable
modelstate<-yuima@model@solve.variable
tmp.env<-new.env()
#if(joint){
coeffic<- coef(res)
# }else{
# coeffic<- res[[1]]
# if(length(res)>1){
# for(j in c(2:length(res))){
# coeffic<-c(coeffic,res[[j]])
# }
# }
#
#}
mp<-match(names(coeffic),parameter)
esort <- coeffic[order(mp)]
for(i in 1:length(coeffic))
{
assign(parameter[i],esort[[i]],envir=tmp.env)
}
# DRIFT <- yuima@model@drift
# JUMP <- yuima@model@jump.coeff
if(length(yuima@model@solve.variable)==1){
#parameter<-yuima@model@parameter@all
#resi<-double(s.size-1)
assign(modeltime,yuima@sampling@delta,envir=tmp.env)
h<-yuima@sampling@delta
assign(modelstate,pX,envir=tmp.env)
jump.term<-eval(JUMP[[1]],envir=tmp.env)
drif.term<-eval(DRIFT,envir=tmp.env)
if(length(jump.term)==1){
jump.term <- rep(jump.term, s.size-1)
}
if(length(drif.term)==1){
drif.term <- rep(drif.term, s.size-1)
} # vectorization (note. if an expression type object does not include state.variable, the length of the item after "eval" operation is 1.)
# for(s in 1:(s.size-1)){
# nova<-sqrt((jump.term)^2) # normalized variance
# resi[s]<-(1/(nova[s]))*(inc[s]-h*drif.term[s])
# }
nova<-sqrt((jump.term)^2)
resi<-(1/(nova[1:(s.size-1)]))*(inc[1:(s.size-1)]-h*drif.term[1:(s.size-1)])
if(length(oldyuima@data@zoo.data)==1){
coefSigdiff<- 1/h*sum(resi^4) #389 resi
coefDriftSig <- 1/h*sum(resi^3)
}
if(aggregation){
Ter <- yuima@sampling@Terminal
ures <- numeric(floor(Ter))
for(l in 1:floor(Ter)){
ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
}
res.incr<-ures
}else{
res.incr<-resi
}
}else{
h<-yuima@sampling@delta
Tbig<-dim(inc)[1]
assign(modeltime,h,envir=tmp.env)
numbofvar<- length(modelstate)
for(j in c(1:numbofvar)){
assign(modelstate[j],pX[,j],envir=tmp.env)
}
drif.term<-array(0,c(Tbig,numbofvar))
for(i in c(1:numbofvar))
drif.term [,i]<- eval(DRIFT[i],envir=tmp.env)
# Check using variable in the drift
# jump.term<-sapply(1:numbofvar,function(i){
# sapply(1:numbLev, function(j){
# eval(JUMP[[i]][j],envir=tmp.env)
# },simplify = TRUE)
# },simplify = TRUE)
jump.term<-array(0,c(numbofvar,numbLev,Tbig))
for(i in c(1:numbofvar)){
for(j in c(1:numbLev))
jump.term[i,j, ] <- eval(JUMP[[i]][j],envir=tmp.env)
}
# if(dim(jump.term)[1]==numbofvar){
# if(dim(jump.term)[2]==numbofvar){
# if(det(jump.term)==0){
# Invjump.term<-solve(t(jump.term)%*%jump.term)%*%t(jump.term)
# }else{
# Invjump.term<-solve(jump.term)
# }
# }else{
# Invjump.term<-solve(t(jump.term)%*%jump.term)%*%t(jump.term)
# }
# Invjump.term <- Invjump.term%o%rep(1,Tbig)
# }else{
#
# }
#
DeltaInc<-(inc-drif.term*h)
if(dim(jump.term)[1]==numbofvar){
if(dim(jump.term)[2]==numbofvar){
resi<-t(sapply(i:Tbig,function(i){
if(det(jump.term[,,i])==0){
step1<-t(jump.term[,,i])%*%jump.term[,,i]
if(det(step1)==0){
Invjump.term<-diag(rep(1,dim(step1)[1]))
}else{
Invjump.term<-solve(step1)%*%t(jump.term[,,i])
}
}else{
Invjump.term<-solve(jump.term[,,i])
}
Invjump.term%*% DeltaInc[i,]
}
)
)
}else{
resi<-t(sapply(i:Tbig,function(i){
step1<-t(jump.term[,,i])%*%jump.term[,,i]
if(det(step1)==0){
Invjump.term<-diag(rep(1,dim(step1)[1]))
}else{
Invjump.term<-solve(step1)%*%t(jump.term[,,i])
}
Invjump.term%*% DeltaInc[i,]
}
)
)
}
}
if(aggregation){
Ter <- min(floor(yuima@sampling@Terminal))
res.incr<-t(sapply(1:Ter,function(i) colSums(resi[(floor((i-1)/h)):(floor(i/h)-1),]) ))
}else{
res.incr<-resi
}
}
if(aggregation){
if(!is.matrix(res.incr)){
res.incr<- as.matrix(res.incr)
}
if(dim(res.incr)[2]==1){
colnames(res.incr)<-sdeModel@jump.variable
}else{
colnames(res.incr)<-paste0(sdeModel@jump.variable,c(1:dim(res.incr)[2]))
}
Incr.Lev <- zooreg(data=res.incr)
Incr.Lev<- setData(original.data = Incr.Lev)
}else{
Incr.Lev <- zoo(res.incr,order.by=yuima@sampling@grid[[1]][-1])
Incr.Lev <- setData(original.data=Incr.Lev)
}
if(length(oldyuima@data@zoo.data)==1){
mydiff<-oldyuima@model@jump.coeff[[1]]
mydiffDer <-deriv(mydiff,oldyuima@model@parameter@jump)
myenvdiff<- new.env()
if(length(oldyuima@model@parameter@jump)>=1){
for(i in c(1:length(oldyuima@model@parameter@jump))){
assign(value=coef[oldyuima@model@parameter@jump[i]],x=oldyuima@model@parameter@jump[i],envir=myenvdiff)
}
}
EvalPartDiff <- Vectorize(FUN= function(myenvdiff,mydiffDer, data){
assign(x=oldyuima@model@solve.variable, value=data,envir = myenvdiff)
return(attr(eval(mydiffDer, envir=myenvdiff),"gradient"))},vectorize.args = "data")
DiffJumpCoeff<-EvalPartDiff(myenvdiff,mydiffDer, data=pX)
if(!is.matrix(DiffJumpCoeff)){
sigmadiffhat<- as.matrix(sum(DiffJumpCoeff^2/jump.term[1:(oldyuima@sampling@n-1)]^2)/(oldyuima@sampling@n))*coefSigdiff
DiffJumpCoeff<- t(DiffJumpCoeff)
}else{
sigmadiffhat<- matrix(0,dim(DiffJumpCoeff)[1],dim(DiffJumpCoeff)[1])
for(t in c(1:dim(DiffJumpCoeff)[2])){
sigmadiffhat <-sigmadiffhat+as.matrix(DiffJumpCoeff[,t])%*%DiffJumpCoeff[,t]/jump.term[t]^2
}
sigmadiffhat<- sigmadiffhat/(oldyuima@sampling@n)*coefSigdiff
}
mydrift<-oldyuima@model@drift[[1]]
mydriftDer <-deriv(mydrift,oldyuima@model@parameter@drift)
myenvdrift<- new.env()
if(length(oldyuima@model@parameter@drift)>=1){
for(i in c(1:length(oldyuima@model@parameter@drift))){
assign(value=coef[oldyuima@model@parameter@drift[i]],x=oldyuima@model@parameter@drift[i],envir=myenvdrift)
}
}
DriftDerCoeff<-EvalPartDiff(myenvdrift,mydriftDer, data=pX)
if(!is.matrix(DriftDerCoeff)){
# sigmadrifthat<- as.matrix(sum(DriftDerCoeff^2/jump.term[1:(oldyuima@sampling@n-1)]^2)/(oldyuima@sampling@n))*coefDriftSig
sigmadrifthat<- as.matrix(sum(DriftDerCoeff^2/jump.term[1:(oldyuima@sampling@n-1)]^2)/(oldyuima@sampling@n))
DriftDerCoeff <- t(DriftDerCoeff)
}else{
sigmadrifthat<- matrix(0,dim(DriftDerCoeff)[1],dim(DriftDerCoeff)[1])
for(t in c(1:dim(DriftDerCoeff)[2])){
sigmadrifthat <-sigmadrifthat+as.matrix(DriftDerCoeff[,t])%*%DriftDerCoeff[,t]/jump.term[t]^2
}
sigmadrifthat<- sigmadrifthat/(oldyuima@sampling@n)
}
sigmadriftdiff <- matrix(0, dim(sigmadrifthat)[2],dim(sigmadiffhat)[1])
for(t in c(1:dim(DriftDerCoeff)[2]))
sigmadriftdiff<-sigmadriftdiff+DriftDerCoeff[,t]%*%t(DiffJumpCoeff[,t])
#sigmadriftdiff<-sigmadriftdiff/oldyuima@sampling@n
sigmadriftdiff<-sigmadriftdiff/oldyuima@sampling@n*coefDriftSig
MatSigmaHat <- rbind(cbind(sigmadiffhat,t(sigmadriftdiff)),cbind(sigmadriftdiff,sigmadrifthat))
res@coef<-res@coef[c(oldyuima@model@parameter@jump,oldyuima@model@parameter@drift)]
res@vcov<-solve(t(myGamhat)%*%solve(MatSigmaHat)%*%myGamhat*oldyuima@sampling@Terminal)
}
if(Est.Incr == "Incr"){
if(length(oldyuima@data@zoo.data)==1){
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
Data = yuima@data, yuima=res)
}else{
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
Data = yuima@data, yuima=res)
vcovLevyNoMeas <- function(myres, Gammahat0, sq=TRUE){
#myres <- res.VG2
DeltaX <- apply(myres@Data@original.data,2,diff)
myData<- myres@Data@original.data
CmatExpr<- myres@model@jump.coeff
ncolC <-length(myres@model@jump.coeff[[1]])
param <- myres@coef[myres@model@parameter@jump]
aexpr<- myres@model@drift
namedrift<-myres@model@parameter@drift
pardrif <- myres@coef[namedrift]
avect_exp<-myres@model@drift
Jac_Drift <- function(aexpr,namedrift,nobs=length(aexpr)){
lapply(X=c(1:nobs),FUN=function(X,namedrift,aexpr){
return(deriv(aexpr[X],namedrift))
},namedrift=namedrift,aexpr=aexpr)
}
Jac_DriftExp <- Jac_Drift(aexpr=avect_exp,namedrift)
FUNDum<-function(foo,myenv) sapply(foo, function(x,env) eval(x,envir = env), env= myenv)
h<-diff(time(myres@Data@zoo.data[[1]]))[1]
dummyf1n<- function(DeltaX, Cmat, h){
C2<-t(Cmat)%*%Cmat
dec <- chol(C2) # Eventualy Add a tryCatch
tmp <- t(DeltaX)%*%solve(C2)%*%DeltaX
logretval <- -h*sum(log(diag(dec))) - 0.5 * as.numeric(tmp)
return(logretval)
}
dummyInc<- function(DeltaX,Cmat, avect,h,sq=TRUE){
if(sq){
Incr <- solve(Cmat)%*%(DeltaX-avect*h)
}else{
C2<-t(Cmat)%*%Cmat
Incr <- solve(C2)%*%Cmat%*%(DeltaX-avect*h)
}
return(Incr)
}
dummyf2n<- function(DeltaX, avect, Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
tmp <- t(Incr)%*%solve(C2)%*%Incr
logretval <- - 0.5/h * as.numeric(tmp)
return(logretval)
}
dumGrad_f2n<-function(DeltaX, avect, Jac_a,Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
Grad<-t(Jac_a)%*%solve(C2)%*%Incr
return(Grad)
}
f1n_j<-function(x, myObsDelta, CmatExpr,h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef )
return(dummyf1n(DeltaX=myObsDelta, Cmat=Cmat, h=h))
}
Incr_Func <- function(x, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq=TRUE){
names(myData)<-myres@model@solve.variable
newenv <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenv )
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenv)
}
return(dummyInc(DeltaX= myObsDelta,Cmat, avect,h,sq=sq))
}
f2n_j <- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
}
return(dummyf2n(DeltaX=myObsDelta, avect=avect, Cmat=Cmat, h=h))
}
Gradf2n_j <-function(x, parDiff, myObsDelta, CmatExpr,
avect_exp, Jac_DriftExp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
Jac_a<- matrix(0,dd,length(x))
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
Jac_a[j,]<-attr(eval(Jac_DriftExp[[j]],envir=newenvDriftCoef),"gradient")
}
return(dumGrad_f2n(DeltaX=myObsDelta, avect=avect, Jac_a=Jac_a, Cmat=Cmat, h=h))
}
# f1n_j(x=param, myObsDelta=DeltaX[1,], CmatExpr=CmatExpr, h=h)
#i=1
# debug(dummyInc)
# Incr_Func(x=c(param,pardrif), myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, sq=TRUE)
# f1n_j(x=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,], myres=myres)
# f2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, avect_exp=avect_exp,
# h=h, myData=myData[i,], myres=myres)
# Gradf2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
# avect_exp, Jac_DriftExp, h, myData[i,], myres)
del <- 10^-3
dummy <- t(rep(1,length(param)))
myeta<- as.matrix(param)%*%dummy
dummyG <- t(rep(1,length(c(param,pardrif))))
globalmyeta <- as.matrix(c(param,pardrif))%*%dummyG
Incr <- del*diag(rep(1,dim(myeta)[1]))
GlobIncr <- del*diag(rep(1,dim(globalmyeta)[1]))
Sigma_gamma <- matrix(0 ,length(param),length(param))
Sigma_alpha <- matrix(0 ,length(pardrif),length(pardrif))
Sigma_algam <- matrix(0 ,length(pardrif),length(param))
histDeltaf1n_j_delta <-matrix(0 , dim(DeltaX)[1],length(param))
histDeltaf2n_j_delta <- matrix(0 , dim(DeltaX)[1],length(pardrif))
# histb_incr <- array(0, c(dim(DeltaX)[2],dim(DeltaX)[1],length(c(param,pardrif))))
for(i in c(1:dim(DeltaX)[1])){
Deltaf1n_j_delta<-sapply(X=1:dim(myeta)[1],
FUN = function(X,myObsDelta, CmatExpr, h, myData, myres,del){
par1<-myeta[,X]+Incr[,X]
#par[oldyuima@model@measure$df@time.var]<-1
f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
par2<-myeta[,X]-Incr[,X]
f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,],
myres=myres, del=del)
# DeltaInc <- sapply(X=1:dim(GlobIncr)[1],
# FUN = function(X, myObsDelta, CmatExpr,avect_exp, h,
# myData, myres, del, sq){
# par1<-globalmyeta[,X]+GlobIncr[,X]
#
# # f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
# f1<-Incr_Func(x=par1, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
# par2<-globalmyeta[,X]-GlobIncr[,X]
# f2<-Incr_Func(x=par2, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
# #f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
# return((f1-f2)/(2*del))
# },
# myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, del=del,sq=sq
# )
#
# histDeltaf1n_j_delta[i, ]<-Deltaf1n_j_delta
#histb_incr[ , i, ] <- DeltaInc
Sigma_gamma <- Sigma_gamma + as.matrix(Deltaf1n_j_delta)%*%t(Deltaf1n_j_delta)
Deltaf2n_j_delta<- Gradf2n_j(x=pardrif, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
avect_exp, Jac_DriftExp, h, myData[i,], myres)
histDeltaf2n_j_delta[i,]<-Deltaf2n_j_delta
Sigma_alpha <- Sigma_alpha + Deltaf2n_j_delta%*%t(Deltaf2n_j_delta)
Sigma_algam <- Sigma_algam + Deltaf2n_j_delta%*%t(Deltaf1n_j_delta)
#cat("\n",i)
}
Tn<-tail(time(myres@Data@original.data),1L)
Sigma_gamma0<-Sigma_gamma/Tn
Sigma_alpha0 <- Sigma_alpha/Tn
Sigma_algam0 <- Sigma_algam/Tn
Sigma0 <- cbind(rbind(Sigma_gamma0,Sigma_algam0),rbind(t(Sigma_algam0),Sigma_alpha0))
InvGammaHAT <- solve(Gammahat0)
vcov <- InvGammaHAT %*% Sigma0 %*% InvGammaHAT/Tn
myres@vcov<- vcov
return(myres)
}
if(length(result@model@jump.coeff)==length(result@model@jump.coeff[[1]])){
sq<-TRUE
}else{
sq<-FALSE
}
result<-vcovLevyNoMeas(myres=result, Gammahat0=myGamhat, sq=sq)
}
return(result)
}
cat("\nEstimation Levy parameters ... \n")
#if(class(mylaw)=="yuima.law"){
if(inherits(mylaw, "yuima.law")){ # YK, Mar. 22, 2022
if(aggregation){
minusloglik <- function(para){
para[length(para)+1]<-1
names(para)[length(para)]<-yuima@model@time.variable
-sum(dens(object=mylaw, x=res.incr, param = para, log = TRUE),
na.rm = T)
}
}else{
minusloglik <- function(para){
para[length(para)+1] <- yuima@sampling@delta
names(para)[length(para)]<-yuima@model@time.variable
-sum(dens(object=mylaw, x=res.incr, param = para, log = TRUE),
na.rm = T)
}
}
para <- start0[lev.names]
lowerjump <- lower0[lev.names]
upperjump <- upper0[lev.names]
esti <- optim(fn = minusloglik, lower = lowerjump, upper = upperjump,
par = para, method = "L-BFGS-B")
HessianEta <- optimHess(par=esti$par, fn=minusloglik)
res@coef<-c(res@coef,esti$par)
res@fullcoef[names(para)]<-esti$par
if(length(oldyuima@data@zoo.data)==1 & is(oldyuima@model@measure$df, "yuima.law")){
if(!aggregation){
Ter <- yuima@sampling@Terminal
ures <- numeric(floor(Ter))
for(l in 1:floor(Ter)){
ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
}
}
mypar<-res@coef[oldyuima@model@parameter@measure]
mypar[oldyuima@model@measure$df@time.var]<-1
fdataeta<-dens(object=oldyuima@model@measure$df,x=ures,param=mypar)# f(eps, eta)
del <- 10^-3
fdatadeltaeta<- dens(object=oldyuima@model@measure$df,x=ures+del,param=mypar) # f(eps + delta, eta)
dummy <- t(rep(1,length(mypar[oldyuima@model@measure$df@param.measure])))
myeta<- as.matrix(mypar[oldyuima@model@measure$df@param.measure])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[oldyuima@model@measure$df@time.var]<-1
dens(object=oldyuima@model@measure$df,x=ures,param=par)
}
)# f(eps, eta+delta)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[oldyuima@model@measure$df@time.var]<-1
dens(object=oldyuima@model@measure$df,x=ures+del,param=par)
}
) # f(eps +deta, eta+delta)
term1<-1/(fdataeta)
term2 <- fdatadeltaeta*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial<-t((as.matrix(term1)%*%dummy)/del^2*term2/oldyuima@sampling@Terminal)
# construction of b_i
# DiffJumpCoeff, DriftDerCoeff, jump.term length(resi)
# step1 <- t(DiffJumpCoeff)%*%DiffJumpCoeff
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/oldyuima@sampling@Terminal
#SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term[-length(jump.term)]^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha <- SigmaEtaAlpha*sum(resi^3)/oldyuima@sampling@delta
b_i <- matrix(0,floor(Ter),length(c(oldyuima@model@parameter@drift, oldyuima@model@parameter@jump)))
Coef1 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@jump))
Coef2 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@drift))
for(l in 1:floor(Ter)){
pos <- (floor((l-1)/h)):(floor(l/h)-1)
if(length(oldyuima@model@parameter@jump)==1){
b_i[l,1:length(oldyuima@model@parameter@jump)] <- sum(-DiffJumpCoeff[,pos]*resi[pos]/jump.term[pos])
Coef1[l,]<-sum(DiffJumpCoeff[,pos]/jump.term[pos]*(resi[pos]^2-h))
}else{
interm <- as.matrix(resi[pos]/jump.term[pos])
b_i[l,1:length(oldyuima@model@parameter@jump)] <- -t(DiffJumpCoeff[,pos]%*%interm)
interm2 <- as.matrix((resi[pos]^2-h)/jump.term[pos])
Coef1[l,] <-DiffJumpCoeff[,pos]%*%interm2
}
if(length(oldyuima@model@parameter@drift)==1){
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <- -sum(h* DriftDerCoeff[,pos]%*%jump.term[pos])
Coef2[l,]<-sum(DriftDerCoeff[,pos]/jump.term[pos]*(resi[pos]))
}else{
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <--h* DriftDerCoeff[,pos]%*%jump.term[pos]
interm3 <- as.matrix((resi[pos])/jump.term[pos])
Coef2[l,] <-DriftDerCoeff[,pos]%*%interm3
}
}
MatrUnder <- mixpartial%*%b_i
I_n <- cbind(rbind(myGamhat,MatrUnder),rbind(matrix(0, dim(myGamhat)[1],dim(HessianEta)[2]),HessianEta/oldyuima@sampling@Terminal))
SigmaGammaEta <- t(DerMeta)%*%Coef1/Ter
SigmaAlphaEta <- t(DerMeta)%*%Coef2/Ter
# dim(fdataetadelta), length(fdataeta), length(term1)
dum <- cbind(SigmaGammaEta , SigmaAlphaEta)
MatSigmaHat1<- rbind(cbind(MatSigmaHat,t(dum)),cbind(dum,SigmaEta))
InvIn<- solve(I_n)
res@vcov <-InvIn%*%MatSigmaHat1%*%t(InvIn)/Ter
colnames(res@vcov)<-names(res@fullcoef)
#res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
rownames(res@vcov)<-names(res@fullcoef)
res@min<-c(res@min,esti$value)
res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
minusloglLevy = minusloglik,logL.Incr=-esti$value,
Data = yuima@data, yuima=res, Levydetails=esti)
}else{
Tn<-yuima@sampling@Terminal
HessianEta_divTn <- HessianEta/Tn
if(!aggregation){
Ter <- min(floor(yuima@sampling@Terminal))
ures<-t(sapply(1:Ter,function(i) colSums(resi[(floor((i-1)/h)):(floor(i/h)-1),]) ))
#yuima.stop("da fare")
vcovLevy1 <- function(myres, HessianEta_divTn, Gammahat0, ures, sq=TRUE){
#myres <- res.VG2
DeltaX <- apply(myres@Data@original.data,2,diff)
myData<- myres@Data@original.data
CmatExpr<- myres@model@jump.coeff
ncolC <-length(myres@model@jump.coeff[[1]])
param <- myres@coef[myres@model@parameter@jump]
aexpr<- myres@model@drift
namedrift<-myres@model@parameter@drift
pardrif <- myres@coef[namedrift]
avect_exp<-myres@model@drift
Jac_Drift <- function(aexpr,namedrift,nobs=length(aexpr)){
lapply(X=c(1:nobs),FUN=function(X,namedrift,aexpr){
return(deriv(aexpr[X],namedrift))
},namedrift=namedrift,aexpr=aexpr)
}
Jac_DriftExp <- Jac_Drift(aexpr=avect_exp,namedrift)
FUNDum<-function(foo,myenv) sapply(foo, function(x,env) eval(x,envir = env), env= myenv)
h<-diff(time(myres@Data@zoo.data[[1]]))[1]
dummyf1n<- function(DeltaX, Cmat, h){
C2<-t(Cmat)%*%Cmat
dec <- chol(C2) # Eventualy Add a tryCatch
tmp <- t(DeltaX)%*%solve(C2)%*%DeltaX
logretval <- -h*sum(log(diag(dec))) - 0.5 * as.numeric(tmp)
return(logretval)
}
dummyInc<- function(DeltaX,Cmat, avect,h,sq=TRUE){
if(sq){
Incr <- solve(Cmat)%*%(DeltaX-avect*h)
}else{
C2<-t(Cmat)%*%Cmat
Incr <- solve(C2)%*%Cmat%*%(DeltaX-avect*h)
}
return(Incr)
}
dummyf2n<- function(DeltaX, avect, Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
tmp <- t(Incr)%*%solve(C2)%*%Incr
logretval <- - 0.5/h * as.numeric(tmp)
return(logretval)
}
dumGrad_f2n<-function(DeltaX, avect, Jac_a,Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
Grad<-t(Jac_a)%*%solve(C2)%*%Incr
return(Grad)
}
f1n_j<-function(x, myObsDelta, CmatExpr,h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef )
return(dummyf1n(DeltaX=myObsDelta, Cmat=Cmat, h=h))
}
Incr_Func <- function(x, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq=TRUE){
names(myData)<-myres@model@solve.variable
newenv <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenv )
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenv)
}
return(dummyInc(DeltaX= myObsDelta,Cmat, avect,h,sq=sq))
}
f2n_j <- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
}
return(dummyf2n(DeltaX=myObsDelta, avect=avect, Cmat=Cmat, h=h))
}
Gradf2n_j <-function(x, parDiff, myObsDelta, CmatExpr,
avect_exp, Jac_DriftExp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
Jac_a<- matrix(0,dd,length(x))
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
Jac_a[j,]<-attr(eval(Jac_DriftExp[[j]],envir=newenvDriftCoef),"gradient")
}
return(dumGrad_f2n(DeltaX=myObsDelta, avect=avect, Jac_a=Jac_a, Cmat=Cmat, h=h))
}
# f1n_j(x=param, myObsDelta=DeltaX[1,], CmatExpr=CmatExpr, h=h)
#i=1
# debug(dummyInc)
# Incr_Func(x=c(param,pardrif), myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, sq=TRUE)
# f1n_j(x=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,], myres=myres)
# f2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, avect_exp=avect_exp,
# h=h, myData=myData[i,], myres=myres)
# Gradf2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
# avect_exp, Jac_DriftExp, h, myData[i,], myres)
del <- 10^-3
dummy <- t(rep(1,length(param)))
myeta<- as.matrix(param)%*%dummy
dummyG <- t(rep(1,length(c(param,pardrif))))
globalmyeta <- as.matrix(c(param,pardrif))%*%dummyG
Incr <- del*diag(rep(1,dim(myeta)[1]))
GlobIncr <- del*diag(rep(1,dim(globalmyeta)[1]))
Sigma_gamma <- matrix(0 ,length(param),length(param))
Sigma_alpha <- matrix(0 ,length(pardrif),length(pardrif))
Sigma_algam <- matrix(0 ,length(pardrif),length(param))
histDeltaf1n_j_delta <-matrix(0 , dim(DeltaX)[1],length(param))
histDeltaf2n_j_delta <- matrix(0 , dim(DeltaX)[1],length(pardrif))
histb_incr <- array(0, c(dim(DeltaX)[2],dim(DeltaX)[1],length(c(param,pardrif))))
for(i in c(1:dim(DeltaX)[1])){
Deltaf1n_j_delta<-sapply(X=1:dim(myeta)[1],
FUN = function(X,myObsDelta, CmatExpr, h, myData, myres,del){
par1<-myeta[,X]+Incr[,X]
#par[oldyuima@model@measure$df@time.var]<-1
f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
par2<-myeta[,X]-Incr[,X]
f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,],
myres=myres, del=del)
DeltaInc <- sapply(X=1:dim(GlobIncr)[1],
FUN = function(X, myObsDelta, CmatExpr,avect_exp, h,
myData, myres, del, sq){
par1<-globalmyeta[,X]+GlobIncr[,X]
# f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
f1<-Incr_Func(x=par1, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
par2<-globalmyeta[,X]-GlobIncr[,X]
f2<-Incr_Func(x=par2, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
#f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, del=del,sq=sq
)
histDeltaf1n_j_delta[i, ]<-Deltaf1n_j_delta
histb_incr[ , i, ] <- DeltaInc
Sigma_gamma <- Sigma_gamma + as.matrix(Deltaf1n_j_delta)%*%t(Deltaf1n_j_delta)
Deltaf2n_j_delta<- Gradf2n_j(x=pardrif, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
avect_exp, Jac_DriftExp, h, myData[i,], myres)
histDeltaf2n_j_delta[i,]<-Deltaf2n_j_delta
Sigma_alpha <- Sigma_alpha + Deltaf2n_j_delta%*%t(Deltaf2n_j_delta)
Sigma_algam <- Sigma_algam + Deltaf2n_j_delta%*%t(Deltaf1n_j_delta)
#cat("\n",i)
}
Tn<-tail(time(myres@Data@original.data),1L)
Sigma_gamma0<-Sigma_gamma/Tn
Sigma_alpha0 <- Sigma_alpha/Tn
Sigma_algam0 <- Sigma_algam/Tn
Sigma0 <- cbind(rbind(Sigma_gamma0,Sigma_algam0),rbind(t(Sigma_algam0),Sigma_alpha0))
myLogDens <- function(x, myObsDelta, CmatExpr,h,myData, myres, pos){
return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
myLogDens2<- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres, pos){
return(f2n_j(x, parDiff, myObsDelta[pos, ], CmatExpr, avect_exp, h, myData[pos,], myres))
#return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
VectLogDens<-Vectorize(FUN=myLogDens,vectorize.args = "pos")
#VectLogDens2<-Vectorize(FUN=myLogDens2,vectorize.args = "pos")
mylogLik<- function(par,DeltaX,CmatExpr, myData, myres, h, Tn, nobs=dim(DeltaX)[1]){
term<-VectLogDens(x=par,
myObsDelta=DeltaX, CmatExpr=CmatExpr,h=h, myData=myData, myres=myres,pos=c(1:nobs))
return(sum(term)/Tn)
}
mylogLik2<- function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
# term<-VectLogDens2(x=par, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres,
# pos=c(1:nobs))
term<-0
for(j in c(1:nobs)){
term<-term+f2n_j(x=par, parDiff, myObsDelta[j, ], CmatExpr, avect_exp, h, myData[j,], myres)
}
return(term/Tn)
}
GradlogLik2<-function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
term<-matrix(0, length(par),1)
for(j in c(1:nobs)){
term <- term + Gradf2n_j(x=par, parDiff, myObsDelta=myObsDelta[j, ], CmatExpr,
avect_exp, Jac_DriftExp, h, myData=myData[j,], myres)
}
return(as.numeric(term)/Tn)
}
# Gammahat <- optimHess(par=param,fn=mylogLik,
# DeltaX=DeltaX,CmatExpr=CmatExpr,
# h=h, Tn=Tn, nobs=dim(DeltaX)[1],
# myData=myData, myres=myres)
# GammaAlfahat <- optimHess(par=pardrif,fn=mylogLik2,gr=GradlogLik2,
# parDiff=param, myObsDelta=DeltaX,
# CmatExpr=CmatExpr, avect_exp=avect_exp, h=h,
# Tn=Tn, nobs=dim(DeltaX)[1], myData=myData, myres=myres)
#
# Gammahat0 <- cbind(rbind(Gammahat,matrix(0,dim(GammaAlfahat)[1],dim(Gammahat)[2])),
# rbind(matrix(0,dim(Gammahat)[2],dim(GammaAlfahat)[1]),GammaAlfahat))
uhistDeltaf1n_j<- matrix(0,floor(Tn),length(param))
uhistDeltaf2n_j<- matrix(0,floor(Tn),length(pardrif))
aaa<-length(c(param,pardrif))
uhistb_incr <- array(0, c(dim(DeltaX)[2],floor(Tn),aaa))
for(l in 1:floor(Tn)){
#ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
uhistDeltaf1n_j[l, ] <- colSums(histDeltaf1n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
uhistDeltaf2n_j[l, ] <- colSums(histDeltaf2n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
for(i in c(1:aaa)){
dumIn <- histb_incr[,(floor((l-1)/h)):(floor(l/h)-1),i]
uhistb_incr[,l,i]<- rowSums(dumIn)
}
}
nMeaspar<-myres@model@parameter@measure
mypar_meas0 <- myres@coef[nMeaspar]#res@coef[oldyuima@model@parameter@measure]
mypar_meas <- c(mypar_meas0,1)
# ures<-myres@Incr.Lev@original.data
names(mypar_meas)<-c(nMeaspar,myres@model@measure$df@time.var)
fdataeta<-dens(object=myres@model@measure$df,x=ures,param=mypar_meas)# f(eps, eta)
del <- 10^-3
dummy <- t(rep(1,length(mypar_meas[myres@model@measure$df@param.measure])))
myeta<- as.matrix(mypar_meas[myres@model@measure$df@param.measure])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures,param=par)
}
)# f(eps, eta+delta)
term1<-1/(fdataeta)
dummyvecdel<-numeric(length=dim(ures)[2])
fdatadeltaeta<- matrix(0,floor(Tn),dim(ures)[2])
mixpartial <-array(0,c(length(nMeaspar),floor(Tn),dim(ures)[2]))
for(j in c(1:dim(ures)[2])){
dummyvecdel[j]<-del
fdatadeltaeta[,j]<- dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=mypar_meas)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=par)
}
) # f(eps +deta, eta+delta)
dummyvecdel<-numeric(length=dim(ures)[2])
term2 <- fdatadeltaeta[,j]*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial[,,j]<-t((as.matrix(term1)%*%dummy)/del^2*term2/Tn)
}
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/Tn
minusloglik <- function(para){
para[length(para)+1]<-1
names(para)[length(para)]<-myres@model@time.variable
-sum(dens(object=myres@model@measure$df, x=ures, param = para, log = TRUE),
na.rm = T)/Tn
}
# HessianEta_divTn <- optimHess(par=mypar_meas0, fn=minusloglik)
Gammaeta_theta <- matrix(0,length(mypar_meas0), aaa)
for(t in c(1:floor(Tn))){
Gammaeta_theta<-Gammaeta_theta+mixpartial[,t,]%*%uhistb_incr[,t,]
}
GammaEta_Theta<- -1/Tn*Gammaeta_theta
Sigma_eta_theta<-t(DerMeta)%*%cbind(uhistDeltaf1n_j,uhistDeltaf2n_j)/Tn
Sigma <- cbind(rbind(Sigma0,Sigma_eta_theta),rbind(t(Sigma_eta_theta),SigmaEta))
GammaHAT<-cbind(rbind(Gammahat0, GammaEta_Theta), rbind(t(GammaEta_Theta), HessianEta_divTn))
InvGammaHAT <- solve(GammaHAT)
vcov <- InvGammaHAT %*% Sigma %*% InvGammaHAT/Tn
myres@vcov<- vcov
return(myres)
}
}
res@vcov<-cbind(res@vcov,matrix(NA,ncol=length(esti$par),nrow=dim(res@vcov)[1]))
res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
colnames(res@vcov)<-names(res@fullcoef)
#res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
rownames(res@vcov)<-names(res@fullcoef)
res@min<-c(res@min,esti$value)
res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
minusloglLevy = minusloglik,logL.Incr=-esti$value,
Data = yuima@data, yuima=res, Levydetails=esti)
if(length(result@model@jump.coeff)==length(result@model@jump.coeff[[1]])){
sq<-TRUE
}else{
sq<-FALSE
}
if(!aggregation){
result <- vcovLevy1(myres = result, HessianEta_divTn = HessianEta_divTn,
Gammahat0 = myGamhat, ures = ures, sq=TRUE)
}else{
vcovLevy <- function(myres, HessianEta_divTn, Gammahat0, sq=TRUE){
#myres <- res.VG2
DeltaX <- apply(myres@Data@original.data,2,diff)
myData<- myres@Data@original.data
CmatExpr<- myres@model@jump.coeff
ncolC <-length(myres@model@jump.coeff[[1]])
param <- myres@coef[myres@model@parameter@jump]
aexpr<- myres@model@drift
namedrift<-myres@model@parameter@drift
pardrif <- myres@coef[namedrift]
avect_exp<-myres@model@drift
Jac_Drift <- function(aexpr,namedrift,nobs=length(aexpr)){
lapply(X=c(1:nobs),FUN=function(X,namedrift,aexpr){
return(deriv(aexpr[X],namedrift))
},namedrift=namedrift,aexpr=aexpr)
}
Jac_DriftExp <- Jac_Drift(aexpr=avect_exp,namedrift)
FUNDum<-function(foo,myenv) sapply(foo, function(x,env) eval(x,envir = env), env= myenv)
h<-diff(time(myres@Data@zoo.data[[1]]))[1]
dummyf1n<- function(DeltaX, Cmat, h){
C2<-t(Cmat)%*%Cmat
dec <- chol(C2) # Eventualy Add a tryCatch
tmp <- t(DeltaX)%*%solve(C2)%*%DeltaX
logretval <- -h*sum(log(diag(dec))) - 0.5 * as.numeric(tmp)
return(logretval)
}
dummyInc<- function(DeltaX,Cmat, avect,h,sq=TRUE){
if(sq){
Incr <- solve(Cmat)%*%(DeltaX-avect*h)
}else{
C2<-t(Cmat)%*%Cmat
Incr <- solve(C2)%*%Cmat%*%(DeltaX-avect*h)
}
return(Incr)
}
dummyf2n<- function(DeltaX, avect, Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
tmp <- t(Incr)%*%solve(C2)%*%Incr
logretval <- - 0.5/h * as.numeric(tmp)
return(logretval)
}
dumGrad_f2n<-function(DeltaX, avect, Jac_a,Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
Grad<-t(Jac_a)%*%solve(C2)%*%Incr
return(Grad)
}
f1n_j<-function(x, myObsDelta, CmatExpr,h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef )
return(dummyf1n(DeltaX=myObsDelta, Cmat=Cmat, h=h))
}
Incr_Func <- function(x, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq=TRUE){
names(myData)<-myres@model@solve.variable
newenv <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenv )
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenv)
}
return(dummyInc(DeltaX= myObsDelta,Cmat, avect,h,sq=sq))
}
f2n_j <- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
}
return(dummyf2n(DeltaX=myObsDelta, avect=avect, Cmat=Cmat, h=h))
}
Gradf2n_j <-function(x, parDiff, myObsDelta, CmatExpr,
avect_exp, Jac_DriftExp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
Jac_a<- matrix(0,dd,length(x))
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
Jac_a[j,]<-attr(eval(Jac_DriftExp[[j]],envir=newenvDriftCoef),"gradient")
}
return(dumGrad_f2n(DeltaX=myObsDelta, avect=avect, Jac_a=Jac_a, Cmat=Cmat, h=h))
}
# f1n_j(x=param, myObsDelta=DeltaX[1,], CmatExpr=CmatExpr, h=h)
#i=1
# debug(dummyInc)
# Incr_Func(x=c(param,pardrif), myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, sq=TRUE)
# f1n_j(x=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,], myres=myres)
# f2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, avect_exp=avect_exp,
# h=h, myData=myData[i,], myres=myres)
# Gradf2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
# avect_exp, Jac_DriftExp, h, myData[i,], myres)
del <- 10^-3
dummy <- t(rep(1,length(param)))
myeta<- as.matrix(param)%*%dummy
dummyG <- t(rep(1,length(c(param,pardrif))))
globalmyeta <- as.matrix(c(param,pardrif))%*%dummyG
Incr <- del*diag(rep(1,dim(myeta)[1]))
GlobIncr <- del*diag(rep(1,dim(globalmyeta)[1]))
Sigma_gamma <- matrix(0 ,length(param),length(param))
Sigma_alpha <- matrix(0 ,length(pardrif),length(pardrif))
Sigma_algam <- matrix(0 ,length(pardrif),length(param))
histDeltaf1n_j_delta <-matrix(0 , dim(DeltaX)[1],length(param))
histDeltaf2n_j_delta <- matrix(0 , dim(DeltaX)[1],length(pardrif))
histb_incr <- array(0, c(dim(DeltaX)[2],dim(DeltaX)[1],length(c(param,pardrif))))
for(i in c(1:dim(DeltaX)[1])){
Deltaf1n_j_delta<-sapply(X=1:dim(myeta)[1],
FUN = function(X,myObsDelta, CmatExpr, h, myData, myres,del){
par1<-myeta[,X]+Incr[,X]
#par[oldyuima@model@measure$df@time.var]<-1
f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
par2<-myeta[,X]-Incr[,X]
f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,],
myres=myres, del=del)
DeltaInc <- sapply(X=1:dim(GlobIncr)[1],
FUN = function(X, myObsDelta, CmatExpr,avect_exp, h,
myData, myres, del, sq){
par1<-globalmyeta[,X]+GlobIncr[,X]
# f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
f1<-Incr_Func(x=par1, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
par2<-globalmyeta[,X]-GlobIncr[,X]
f2<-Incr_Func(x=par2, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
#f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, del=del,sq=sq
)
histDeltaf1n_j_delta[i, ]<-Deltaf1n_j_delta
histb_incr[ , i, ] <- DeltaInc
Sigma_gamma <- Sigma_gamma + as.matrix(Deltaf1n_j_delta)%*%t(Deltaf1n_j_delta)
Deltaf2n_j_delta<- Gradf2n_j(x=pardrif, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
avect_exp, Jac_DriftExp, h, myData[i,], myres)
histDeltaf2n_j_delta[i,]<-Deltaf2n_j_delta
Sigma_alpha <- Sigma_alpha + Deltaf2n_j_delta%*%t(Deltaf2n_j_delta)
Sigma_algam <- Sigma_algam + Deltaf2n_j_delta%*%t(Deltaf1n_j_delta)
#cat("\n",i)
}
Tn<-tail(time(myres@Data@original.data),1L)
Sigma_gamma0<-Sigma_gamma/Tn
Sigma_alpha0 <- Sigma_alpha/Tn
Sigma_algam0 <- Sigma_algam/Tn
Sigma0 <- cbind(rbind(Sigma_gamma0,Sigma_algam0),rbind(t(Sigma_algam0),Sigma_alpha0))
myLogDens <- function(x, myObsDelta, CmatExpr,h,myData, myres, pos){
return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
myLogDens2<- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres, pos){
return(f2n_j(x, parDiff, myObsDelta[pos, ], CmatExpr, avect_exp, h, myData[pos,], myres))
#return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
VectLogDens<-Vectorize(FUN=myLogDens,vectorize.args = "pos")
#VectLogDens2<-Vectorize(FUN=myLogDens2,vectorize.args = "pos")
mylogLik<- function(par,DeltaX,CmatExpr, myData, myres, h, Tn, nobs=dim(DeltaX)[1]){
term<-VectLogDens(x=par,
myObsDelta=DeltaX, CmatExpr=CmatExpr,h=h, myData=myData, myres=myres,pos=c(1:nobs))
return(sum(term)/Tn)
}
mylogLik2<- function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
# term<-VectLogDens2(x=par, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres,
# pos=c(1:nobs))
term<-0
for(j in c(1:nobs)){
term<-term+f2n_j(x=par, parDiff, myObsDelta[j, ], CmatExpr, avect_exp, h, myData[j,], myres)
}
return(term/Tn)
}
GradlogLik2<-function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
term<-matrix(0, length(par),1)
for(j in c(1:nobs)){
term <- term + Gradf2n_j(x=par, parDiff, myObsDelta=myObsDelta[j, ], CmatExpr,
avect_exp, Jac_DriftExp, h, myData=myData[j,], myres)
}
return(as.numeric(term)/Tn)
}
# Gammahat <- optimHess(par=param,fn=mylogLik,
# DeltaX=DeltaX,CmatExpr=CmatExpr,
# h=h, Tn=Tn, nobs=dim(DeltaX)[1],
# myData=myData, myres=myres)
# GammaAlfahat <- optimHess(par=pardrif,fn=mylogLik2,gr=GradlogLik2,
# parDiff=param, myObsDelta=DeltaX,
# CmatExpr=CmatExpr, avect_exp=avect_exp, h=h,
# Tn=Tn, nobs=dim(DeltaX)[1], myData=myData, myres=myres)
#
# Gammahat0 <- cbind(rbind(Gammahat,matrix(0,dim(GammaAlfahat)[1],dim(Gammahat)[2])),
# rbind(matrix(0,dim(Gammahat)[2],dim(GammaAlfahat)[1]),GammaAlfahat))
uhistDeltaf1n_j<- matrix(0,floor(Tn),length(param))
uhistDeltaf2n_j<- matrix(0,floor(Tn),length(pardrif))
aaa<-length(c(param,pardrif))
uhistb_incr <- array(0, c(dim(DeltaX)[2],floor(Tn),aaa))
for(l in 1:floor(Tn)){
#ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
uhistDeltaf1n_j[l, ] <- colSums(histDeltaf1n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
uhistDeltaf2n_j[l, ] <- colSums(histDeltaf2n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
for(i in c(1:aaa)){
dumIn <- histb_incr[,(floor((l-1)/h)):(floor(l/h)-1),i]
uhistb_incr[,l,i]<- rowSums(dumIn)
}
}
nMeaspar<-myres@model@parameter@measure
mypar_meas0 <- myres@coef[nMeaspar]#res@coef[oldyuima@model@parameter@measure]
mypar_meas <- c(mypar_meas0,1)
ures<-myres@Incr.Lev@original.data
names(mypar_meas)<-c(nMeaspar,myres@model@measure$df@time.var)
fdataeta<-dens(object=myres@model@measure$df,x=ures,param=mypar_meas)# f(eps, eta)
del <- 10^-3
dummy <- t(rep(1,length(mypar_meas[myres@model@measure$df@param.measure])))
myeta<- as.matrix(mypar_meas[myres@model@measure$df@param.measure])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures,param=par)
}
)# f(eps, eta+delta)
term1<-1/(fdataeta)
dummyvecdel<-numeric(length=dim(ures)[2])
fdatadeltaeta<- matrix(0,floor(Tn),dim(ures)[2])
mixpartial <-array(0,c(length(nMeaspar),floor(Tn),dim(ures)[2]))
for(j in c(1:dim(ures)[2])){
dummyvecdel[j]<-del
fdatadeltaeta[,j]<- dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=mypar_meas)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=par)
}
) # f(eps +deta, eta+delta)
dummyvecdel<-numeric(length=dim(ures)[2])
term2 <- fdatadeltaeta[,j]*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial[,,j]<-t((as.matrix(term1)%*%dummy)/del^2*term2/Tn)
}
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/Tn
minusloglik <- function(para){
para[length(para)+1]<-1
names(para)[length(para)]<-myres@model@time.variable
-sum(dens(object=myres@model@measure$df, x=ures, param = para, log = TRUE),
na.rm = T)/Tn
}
# HessianEta_divTn <- optimHess(par=mypar_meas0, fn=minusloglik)
Gammaeta_theta <- matrix(0,length(mypar_meas0), aaa)
for(t in c(1:floor(Tn))){
Gammaeta_theta<-Gammaeta_theta+mixpartial[,t,]%*%uhistb_incr[,t,]
}
GammaEta_Theta<- -1/Tn*Gammaeta_theta
Sigma_eta_theta<-t(DerMeta)%*%cbind(uhistDeltaf1n_j,uhistDeltaf2n_j)/Tn
Sigma <- cbind(rbind(Sigma0,Sigma_eta_theta),rbind(t(Sigma_eta_theta),SigmaEta))
GammaHAT<-cbind(rbind(Gammahat0, GammaEta_Theta), rbind(t(GammaEta_Theta), HessianEta_divTn))
InvGammaHAT <- solve(GammaHAT)
vcov <- InvGammaHAT %*% Sigma %*% InvGammaHAT/Tn
myres@vcov<- vcov
return(myres)
}
result <- vcovLevy(result,HessianEta_divTn,myGamhat,sq=sq)
}
#result <- vcovLevy(result,HessianEta_divTn,myGamhat,sq=sq)
# colnames(result@vcov)<-names(res@fullcoef)
# rownames(result@vcov)<-names(res@fullcoef)
}
# colnames(res@vcov)<-names(res@fullcoef)
# #res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
# rownames(res@vcov)<-names(res@fullcoef)
# res@min<-c(res@min,esti$value)
# res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
return(result)
}else{
dist <- substr(as.character(orig.mylaw$df$expr), 2, 10^3)
startjump <- start0[lev.names]
lowerjump <- lower0[lev.names]
upperjump <- upper0[lev.names]
if(length(startjump) == -1){
logdens <- function(para){
exlogdens <- parse(text = sprintf("log(d%s)", dist))
assign(myjumpname, ures, envir = tmp.env)
assign(mymeasureparam, para, envir = tmp.env)
sum(eval(exlogdens, envir = tmp.env))
}
mydens <-function(para){
exdens <- parse(text = sprintf("d%s", dist))
assign(myjumpname, ures, envir = tmp.env)
assign(mymeasureparam, para, envir = tmp.env)
eval(exdens, envir = tmp.env)
}
intervaljump <- c(lowerjump[[1]], upperjump[[1]])
esti <- optimize(logdens, interval = intervaljump, maximum = TRUE)
return(list(sde=esort, meas=esti$maximum))
}else{
logdens <- function(para){
exlogdens <- parse(text = sprintf("log(d%s)", dist))
assign(oldyuima@model@jump.variable, ures, envir = tmp.env)
for(i in c(1:length(oldyuima@model@parameter@measure)))
assign(oldyuima@model@parameter@measure[i], para[[oldyuima@model@parameter@measure[i]]], envir = tmp.env)
-sum(eval(exlogdens, envir = tmp.env),na.rm = T)
}
mydens1 <-function(par,x){
exdens <- parse(text = sprintf("d%s", dist))
assign(myjumpname, x, envir = tmp.env)
assign(mymeasureparam, par, envir = tmp.env)
eval(exdens, envir = tmp.env)
}
esti <- optim(fn=logdens, lower = lowerjump, upper = upperjump, par = startjump,
method = "L-BFGS-B")
HessianEta <- optimHess(par=esti$par, fn=logdens)
res@coef<-c(res@coef,esti$par)
res@fullcoef[lev.names]<-esti$par
if(length(oldyuima@data@zoo.data)==1){
if(!aggregation){
Ter <- yuima@sampling@Terminal
ures <- numeric(floor(Ter))
for(l in 1:floor(Ter)){
ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
}
}
mypar<-res@coef[oldyuima@model@parameter@measure]
#mypar[oldyuima@model@measure$df@time.var]<-1
fdataeta<-mydens1(par=mypar,x=ures)# f(eps, eta)
del <- 10^-3
fdatadeltaeta<- mydens1(par=mypar,x=ures+del) # f(eps + delta, eta)
dummy <- t(rep(1,length(mypar[lev.names])))
myeta<- as.matrix(mypar[lev.names])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
#par[oldyuima@model@measure$df@time.var]<-1
mydens1(par=par,x=ures)
}
)# f(eps, eta+delta)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
#par[oldyuima@model@measure$df@time.var]<-1
mydens1(par=par,x=ures+del)
}
) # f(eps +deta, eta+delta)
term1<-1/(fdataeta)
term2 <- fdatadeltaeta*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial<-t((as.matrix(term1)%*%dummy)/del^2*term2/oldyuima@sampling@Terminal)
# construction of b_i
# DiffJumpCoeff, DriftDerCoeff, jump.term length(resi)
# step1 <- t(DiffJumpCoeff)%*%DiffJumpCoeff
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/oldyuima@sampling@Terminal
#SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term[-length(jump.term)]^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha <- SigmaEtaAlpha*sum(resi^3)/oldyuima@sampling@delta
b_i <- matrix(0,floor(Ter),length(c(oldyuima@model@parameter@drift, oldyuima@model@parameter@jump)))
Coef1 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@jump))
Coef2 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@drift))
for(l in 1:floor(Ter)){
pos <- (floor((l-1)/h)):(floor(l/h)-1)
if(length(oldyuima@model@parameter@jump)==1){
b_i[l,1:length(oldyuima@model@parameter@jump)] <- sum(-DiffJumpCoeff[,pos]*resi[pos]/jump.term[pos])
Coef1[l,]<-sum(DiffJumpCoeff[,pos]/jump.term[pos]*(resi[pos]^2-h))
}else{
interm <- as.matrix(resi[pos]/jump.term[pos])
b_i[l,1:length(oldyuima@model@parameter@jump)] <- -t(DiffJumpCoeff[,pos]%*%interm)
interm2 <- as.matrix((resi[pos]^2-h)/jump.term[pos])
Coef1[l,] <-DiffJumpCoeff[,pos]%*%interm2
}
if(length(oldyuima@model@parameter@drift)==1){
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <- -sum(h* DriftDerCoeff[,pos]%*%jump.term[pos])
Coef2[l,]<-sum(DriftDerCoeff[,pos]/jump.term[pos]*(resi[pos]))
}else{
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <--h* DriftDerCoeff[,pos]%*%jump.term[pos]
interm3 <- as.matrix((resi[pos])/jump.term[pos])
Coef2[l,] <-DriftDerCoeff[,pos]%*%interm3
}
}
MatrUnder <- mixpartial%*%b_i
I_n <- cbind(rbind(myGamhat,MatrUnder),rbind(matrix(0, dim(myGamhat)[1],dim(HessianEta)[2]),HessianEta/oldyuima@sampling@Terminal))
SigmaGammaEta <- t(DerMeta)%*%Coef1/Ter
SigmaAlphaEta <- t(DerMeta)%*%Coef2/Ter
# dim(fdataetadelta), length(fdataeta), length(term1)
dum <- cbind(SigmaGammaEta , SigmaAlphaEta)
MatSigmaHat1<- rbind(cbind(MatSigmaHat,t(dum)),cbind(dum,SigmaEta))
InvIn<- solve(I_n)
res@vcov <-InvIn%*%MatSigmaHat1%*%t(InvIn)/Ter
}else{
res@vcov<-cbind(res@vcov,matrix(NA,ncol=length(esti$par),nrow=dim(res@vcov)[1]))
}
colnames(res@vcov)<-names(res@fullcoef)
#res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
rownames(res@vcov)<-names(res@fullcoef)
res@min<-c(res@min,esti$value)
res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
minusloglLevy = logdens,logL.Incr=-esti$value,
Data = yuima@data, yuima=res, Levydetails=esti)
return(result)
#return(list(sde=esort, meas=esti$par))
}
}
}
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Defines functions qmleLevy
Documented in qmleLevy
########################################################################
# Stepwise estimation for ergodic Levy driven SDE
########################################################################
#qmleLevy<-function(yuima,start,lower,upper,joint = FALSE,third = FALSE,
# Est.Incr = c("NoIncr","Incr","IncrPar"),
# aggregation = TRUE)
qmleLevy<-function(yuima,start,lower,upper,joint = FALSE,third = FALSE,
Est.Incr = "NoIncr",
aggregation = TRUE)
{
oldyuima<-yuima #line1
myjumpname <- yuima@model@jump.variable
mymeasureparam <- yuima@model@parameter@measure
if(!(Est.Incr %in% c("NoIncr","Incr","IncrPar")))
stop("Argument'Est.Incr' must be one of \"NoIncr\",\"Incr\" or \"IncrPar\"")
call <- match.call()
truestart<-start
cat("\nStarting QGMLE for SDE ... \n")
parameter<-yuima@model@parameter@all
orig.mylaw<-yuima@model@measure
mylaw<-yuima@model@measure$df
numbLev<-length(yuima@model@measure.type)
if(missing(yuima))
yuima.stop("yuima object is missing.")
if(!is(yuima,"yuima"))
yuima.stop("This function is for yuima-class.")
if(length(yuima@model@parameter@jump)>0)
paracoef <- yuima@model@parameter@jump
if(length(yuima@model@parameter@drift)>0)
paracoef <- c(paracoef, yuima@model@parameter@drift)
if(Est.Incr == "IncrPar"){
start0<-start
lower0<-lower
upper0<-upper
lev.names<-yuima@model@parameter@measure
}
DRIFT <- yuima@model@drift
JUMP <- yuima@model@jump.coeff
sdeModel<-yuima@model
if(length(sdeModel@parameter@measure)!=0){
nPar<-length(sdeModel@parameter@measure)
for(i in c(1:nPar)){
assign(x = sdeModel@parameter@measure[i],
value = start[[sdeModel@parameter@measure[i]]])
}
names1 <- names(start)
index <- which(names1 %in% sdeModel@parameter@measure)
start <- start[-index]
names1 <- names(lower)
index <- which(names1 %in% sdeModel@parameter@measure)
lower <- lower[-index]
names1 <- names(upper)
index <- which(names1 %in% sdeModel@parameter@measure)
upper <- upper[-index]
}
#if(class(sdeModel@measure$df)!="yuima.law"){
if(!inherits(sdeModel@measure$df, "yuima.law")){ # fixed by YK
code <- suppressWarnings(sub("^(.+?)\\(.+", "\\1", sdeModel@measure$df$expr, perl=TRUE))
candinoise<-c("rNIG","rvgamma","rnts","rbgamma")
if(is.na(match(code,candinoise))){
yuima.stop("This function works only for the standardized normal inverse Gaussian process, variance gamma process, bilateral gamma process, and normal tempered stable process now.")
}
if(length(sdeModel@xinit) == 1){
args <- unlist(strsplit(suppressWarnings(sub("^.+?\\((.+)\\)", "\\1", sdeModel@measure$df$expr, perl=TRUE)), ","))
if(code == "rNIG"){
if(!((abs(eval(parse(text = paste("(",args[5] ,")+(", args[3], ")*(", args[4],
")/sqrt((", args[2], ")^2-(", args[3], ")^2)" )))) < 10^(-10))
&& (abs(eval(parse(text = paste("(",args[2], ")^2*(", args[4], ")/(sqrt((", args[2],
")^2-(", args[3], ")^2))^3"))) -1) < 10^(-10))))
{
yuima.stop("This function is only for standardized Levy noises.")
}
}
else if(code == "rvgamma"){
if(!((abs(eval(parse(text = paste("(", args[5], ")+2*(", args[2], ")*(", args[4], ")/((", args[3], ")^2-("
, args[4], ")^2)" )))) < 10^(-10))
&& (abs(eval(parse(text = paste("2*((", args[2], ")*(", args[3], ")^2+(", args[4], ")^2)", "/(("
, args[3], ")^2-(", args[4], ")^2)^2"))) - 1) < 10^(-10))))
{
yuima.stop("This function is only for standardized Levy noises")
}
}
else if((code == "rnts")){
if(!((abs(eval(parse(text = paste("(", args[6], ")-(", args[2], ")*(",
args[3], ")*(", args[4], ")^((", args[2],
")-1)*gamma(1-(", args[2], "))*(-1/(", args[2],"))*(", args[5],
")"
)))) < 10^(-10))
&&(abs(eval(parse(text = paste("(", args[3], ")*(", args[2],")*((", args[2], ")-1)*gamma(1-(", args[2], "))*(-1/(", args[2],"))*(", args[4], ")^((",args[2], ")-2)*(", args[5], ")^2-(",
args[2], ")*(", args[3], ")*(", args[4], ")^((", args[2], ")-1)*gamma(1-(", args[2], "))*(-1/(", args[2],"))"
))) - 1) < 10^(-10))))
{
yuima.stop("This function is only for standardized Levy processes.")
}
}else if(code == "rbgamma"){
if(!((abs(eval(parse(text = paste("(", args[2], ")/(", args[3],")-(", args[4],")/(", args[5], ")")))) < 10^(-10))
&& (abs(eval(parse(text = paste("(", args[2], ")/(", args[3], ")^2","+(", args[4],")/(", args[5],")^2"
))) - 1) < 10^(-10) )))
{
yuima.stop("This function is only for standardized Levy processes.")
}
}
}else{
warning("In this version, the standardized conditions on multidimensional noises can not be verified.
The expressions of mean and variance are given in help page.")
# The noise condition checker below does not work now (YU: 3/23).
# args <- suppressWarnings(sub("^.+?\\((.+)\\)", "\\1", sdeModel@measure$df$expr, perl=TRUE))
# yuimaEnv <- new.env()
# yuimaEnv$mean <- switch(code,
# rNIG = function(x=1,alpha,beta,delta0,mu,Lambda){mu+as.vector(delta0/(sqrt(alpha^2-t(beta)%*%Lambda%*%beta)))*Lambda%*%beta},
# rnts = function(x=1,alpha,a,b,beta,mu,Lambda){mu+gamma(1-alpha)*a*b^(alpha-1)*Lambda%*%beta},
# rvgamma = function(x=1,lambda,alpha,beta,mu,Lambda){mu+as.vector(2*lambda/(alpha^2-t(beta)%*%Lambda%*%beta)^2)*beta}
# )
#
# yuimaEnv$covariance <- switch(code,
# rNIG = function(x=1,alpha,beta,delta0,mu,Lambda){as.vector(delta0/(sqrt(alpha^2-t(beta)%*%Lambda%*%beta))^3)*Lambda%*%beta%*%t(beta)%*%Lambda+as.vector(delta0/sqrt(alpha^2-t(beta)%*%Lambda%*%beta))*Lambda},
# rnts = function(x=1,alpha,a,b,beta,mu,Lambda){a*(1-alpha)*gamma(1-alpha)*b^(alpha-2)*Lambda%*%beta%*%t(beta)%*%Lambda+a*gamma(1-alpha)*b^(alpha-1)*Lambda},
# rvgamma = function(x=1,lambda,alpha,beta,mu,Lambda){as.vector(4*lambda/(alpha^2-t(beta)%*%Lambda%*%beta)^2)*Lambda%*%beta%*%t(beta)%*%Lambda+as.vector(2*lambda/alpha^2-t(beta)%*%Lambda%*%beta)*Lambda}
# )
# judgemean<-sum(eval(parse(text = paste("mean","(",args,")")),yuimaEnv)==numeric(length(sdeModel@xinit)))
# judgecovariance<-sum(eval(eval(parse(text = paste("covariance","(",args,")")),yuimaEnv)==diag(1,length(sdeModel@xinit))))
# if(!((judgemean==length(sdeModel@xinit))&&(judgecovariance==length(sdeModel@xinit)*length(sdeModel@xinit))))
# {
# yuima.stop("This function is only for standardized Levy processes.")
# }
}
}else{fullcoef<-NULL}
yuima@sampling@delta <- yuima@sampling@delta[1]
yuima@model@noise.number <- as.integer(yuima@model@equation.number)
if(!joint){
DRIFT <- yuima@model@drift
DRPAR <- yuima@model@parameter@drift
if(length(yuima@model@parameter@jump)>0)
fullcoef <- yuima@model@parameter@jump
if(length(DRPAR)>0)
fullcoef <- c(fullcoef, DRPAR)
oo <- match(yuima@model@parameter@all, fullcoef)
yuima@model@parameter@all <- yuima@model@parameter@all[order(oo)]
oo <- match(names(start), fullcoef)
start <- start[order(oo)]
oo <- match(names(upper), fullcoef)
upper <- upper[order(oo)]
oo <- match(names(lower), fullcoef)
lower <- lower[order(oo)]
yuima@model@diffusion <- yuima@model@jump.coeff
yuima@model@parameter@diffusion <- yuima@model@parameter@jump[1:length(yuima@model@parameter@jump)]
yuima@model@parameter@all <- yuima@model@parameter@diffusion
for(i in 1:length(yuima@model@drift)){
yuima@model@drift[i] <- expression((0))
}
yuima@model@jump.coeff <- list()
yuima@model@parameter@drift <- character(0)
yuima@model@measure <- list()
yuima@model@jump.variable <- character(0)
yuima@model@measure.type <- character(0)
yuima@model@parameter@jump <- character(0)
yuima@model@parameter@measure <- character(0)
diffstart <- start[1:length(yuima@model@parameter@diffusion)]
diffupper <- upper[1:length(yuima@model@parameter@diffusion)]
difflower <- lower[1:length(yuima@model@parameter@diffusion)]
fres <- qmle(yuima=yuima,start=diffstart,lower=difflower,upper=diffupper,rcpp = TRUE,joint = FALSE,method = "L-BFGS-B")
DiffHessian<- fres@details$hessian #182
DIPAR <- yuima@model@parameter@diffusion
DIFFUSION <- yuima@model@diffusion
yuima@model@parameter@all <- DRPAR
yuima@model@parameter@drift <- DRPAR
yuima@model@drift <- DRIFT
dristart <- start[-(1:length(yuima@model@parameter@diffusion))]
driupper <- upper[-(1:length(yuima@model@parameter@diffusion))]
drilower <- lower[-(1:length(yuima@model@parameter@diffusion))]
partcoef <- yuima@model@parameter@diffusion
ov <- match(yuima@model@parameter@drift,partcoef)
ovp <- which(!is.na(ov))
if(length(ovp)>0)
{yuima@model@parameter@drift <- yuima@model@parameter@drift[-ovp]}
yuima@model@parameter@all <- yuima@model@parameter@drift
ma <- match(names(fres@coef),partcoef)
sort <- fres@coef[order(ma)]
esti <- numeric(length(partcoef))
newdiff <- yuima@model@diffusion
newdri <- yuima@model@drift
for(i in 1:length(partcoef))
{
esti[i] <- as.character(fres@coef[[i]])
}
if(length(yuima@model@drift) == 1){
for(i in 1:length(partcoef))
{
newdri <- gsub(partcoef[i],esti[i],newdri)
yuima@model@drift[1] <- parse(text = newdri[1])
newdiff[[1]] <- gsub(partcoef[i],esti[i],newdiff[[1]])
yuima@model@diffusion[[1]] <- parse(text = newdiff[[1]])
}
}else{
for(i in 1:length(partcoef))
{
for(j in 1:length(yuima@model@drift))
{
newdri[j] <- gsub(partcoef[i],esti[i],newdri[j])
yuima@model@drift[j] <- parse(text = newdri[j])
}
for(k in 1:length(yuima@model@diffusion)){
for(l in 1:length(yuima@model@diffusion[[1]])){
newdiff[[k]][l] <- gsub(partcoef[i],esti[i],newdiff[[k]][l])
yuima@model@diffusion[[k]][l] <- parse(text = newdiff[[k]][l])
}
}
}
}
yuima@model@parameter@diffusion <- character(0)
sres<-qmle(yuima=yuima,start=dristart,lower=drilower,upper=driupper,rcpp = TRUE,method = "L-BFGS-B")
DriftHessian <- sres@details$hessian #239
if((length(ovp) == 0) && (third)){
yuima@model@diffusion <- DIFFUSION
yuima@model@drift <- DRIFT
yuima@model@parameter@diffusion <- DIPAR
yuima@model@parameter@all <- DIPAR
newdri <- yuima@model@drift
for(i in 1:length(sres@coef))
{
esti[i] <- as.character(sres@coef[[i]])
}
if(length(yuima@model@drift)==1){
for(i in 1:length(sres@coef))
{
newdri <- gsub(yuima@model@parameter@drift[i],esti[i],newdri)
yuima@model@drift[1] <- parse(text=newdri[1])
}
}else{
for(i in 1:length(sres@coef))
{
for(j in 1:length(yuima@model@drift))
{
newdri[j] <- gsub(yuima@model@parameter@drift[i],esti[i],newdri[j])
yuima@model@drift[j] <- parse(text = newdri[j])
}
}
}
yuima@model@parameter@drift <- character(0)
too <- match(names(fres@coef),names(diffstart))
diffstart <- diffstart[order(too)]
for(i in 1:length(diffstart)){
diffstart[[i]] <- fres@coef[[i]]
}
tres <- qmle(yuima=yuima,start=diffstart,lower=difflower,upper=diffupper,rcpp = TRUE,joint = FALSE,method = "L-BFGS-B")
res <- list(first = fres@coef, second = sres@coef, third = tres@coef)
}else if((length(ovp) > 0) || !(third)){
coef<-c(sres@coef,fres@coef)
mycoef<-unlist(truestart)
#mycoef1<-mycoef[names(coef)]
mycoef2<-mycoef[!names(mycoef)%in%names(coef)]
mycoef<-c(coef,mycoef2)
vcov0<-matrix(NA,nrow = length(coef),ncol=length(coef))
rownames(vcov0)<-names(coef)
colnames(vcov0)<-names(coef)
min0<- c(fres@min,sres@min)
details0<-list(sres@details,fres@details)
nobs0<-sres@nobs
res<-new("yuima.qmle", call = call, coef = coef, fullcoef = mycoef,
vcov = vcov0, min = min0, details = details0, minuslogl = minusquasilogl,
method = sres@method, nobs=nobs0, model=sdeModel)
# res <- list(first = fres@coef, second = sres@coef)}
if(length(oldyuima@data@zoo.data)==1){
myGamhat <- matrix(0,length(coef),length(coef))
myGamhat[1:dim(DiffHessian)[1],1:dim(DiffHessian)[2]]<-DiffHessian
myGamhat[dim(DiffHessian)[1]+1:dim(DriftHessian)[1],dim(DiffHessian)[1]+1:dim(DriftHessian)[2]]<-DriftHessian#293
myGamhat<-myGamhat/oldyuima@sampling@Terminal
}else{
myGamhat <- matrix(0,length(coef),length(coef))
myGamhat[1:dim(DiffHessian)[1],1:dim(DiffHessian)[2]]<-DiffHessian*oldyuima@sampling@Terminal/oldyuima@sampling@n
myGamhat[dim(DiffHessian)[1]+1:dim(DriftHessian)[1],dim(DiffHessian)[1]+1:dim(DriftHessian)[2]]<-DriftHessian#293
myGamhat<-myGamhat/oldyuima@sampling@Terminal
}
}else{
yuima.stop("third estimation may be theoretical invalid under the presence of an overlapping parameter.")
}
}else{
if(third){
yuima.stop("third estimation does not make sense in joint estimation.")
}
if(length(yuima@model@parameter@jump)>0)
fullcoef <- yuima@model@parameter@jump
if(length(yuima@model@parameter@drift)>0)
fullcoef <- c(fullcoef, yuima@model@parameter@drift)
oo <- match(yuima@model@parameter@all, fullcoef)
yuima@model@parameter@all <- yuima@model@parameter@all[order(oo)]
yuima@model@parameter@all <- yuima@model@parameter@all[1:length(which(!is.na(oo)))]
yuima@model@diffusion <- yuima@model@jump.coeff
yuima@model@jump.coeff <- list()
yuima@model@parameter@diffusion <- yuima@model@parameter@jump[1:length(yuima@model@parameter@jump)]
yuima@model@measure <- list()
yuima@model@jump.variable <- character(0)
yuima@model@measure.type <- character(0)
yuima@model@parameter@jump <- character(0)
yuima@model@parameter@measure <- character(0)
# jres<-qmle(yuima,start = start,lower = lower,upper = upper,rcpp = TRUE, joint = TRUE,method = "L-BFGS-B")
# res<-list(joint = jres@coef)
res<-qmle(yuima,start = start,lower = lower,upper = upper,rcpp = TRUE, joint = TRUE,
method = "L-BFGS-B")
}
if(Est.Incr == "NoIncr"){
return(res)
}
cat("\nStarting Estimation of Levy Increments ... \n")
data <- get.zoo.data(yuima)
s.size<-yuima@sampling@n
if(length(data)==1){
X<-as.numeric(data[[1]])
pX<-X[1:(s.size-1)]
inc<-double(s.size-1)
inc<-X[2:(s.size)]-pX
}else{
pX<- simplify2array(lapply(X = data,
FUN = as.numeric))
pX<-pX[-nrow(pX),]
inc<- simplify2array(lapply(X = data,
FUN = function(X){diff(as.numeric(X))}))
}
modeltime<-yuima@model@time.variable
modelstate<-yuima@model@solve.variable
tmp.env<-new.env()
#if(joint){
coeffic<- coef(res)
# }else{
# coeffic<- res[[1]]
# if(length(res)>1){
# for(j in c(2:length(res))){
# coeffic<-c(coeffic,res[[j]])
# }
# }
#
#}
mp<-match(names(coeffic),parameter)
esort <- coeffic[order(mp)]
for(i in 1:length(coeffic))
{
assign(parameter[i],esort[[i]],envir=tmp.env)
}
# DRIFT <- yuima@model@drift
# JUMP <- yuima@model@jump.coeff
if(length(yuima@model@solve.variable)==1){
#parameter<-yuima@model@parameter@all
#resi<-double(s.size-1)
assign(modeltime,yuima@sampling@delta,envir=tmp.env)
h<-yuima@sampling@delta
assign(modelstate,pX,envir=tmp.env)
jump.term<-eval(JUMP[[1]],envir=tmp.env)
drif.term<-eval(DRIFT,envir=tmp.env)
if(length(jump.term)==1){
jump.term <- rep(jump.term, s.size-1)
}
if(length(drif.term)==1){
drif.term <- rep(drif.term, s.size-1)
} # vectorization (note. if an expression type object does not include state.variable, the length of the item after "eval" operation is 1.)
# for(s in 1:(s.size-1)){
# nova<-sqrt((jump.term)^2) # normalized variance
# resi[s]<-(1/(nova[s]))*(inc[s]-h*drif.term[s])
# }
nova<-sqrt((jump.term)^2)
resi<-(1/(nova[1:(s.size-1)]))*(inc[1:(s.size-1)]-h*drif.term[1:(s.size-1)])
if(length(oldyuima@data@zoo.data)==1){
coefSigdiff<- 1/h*sum(resi^4) #389 resi
coefDriftSig <- 1/h*sum(resi^3)
}
if(aggregation){
Ter <- yuima@sampling@Terminal
ures <- numeric(floor(Ter))
for(l in 1:floor(Ter)){
ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
}
res.incr<-ures
}else{
res.incr<-resi
}
}else{
h<-yuima@sampling@delta
Tbig<-dim(inc)[1]
assign(modeltime,h,envir=tmp.env)
numbofvar<- length(modelstate)
for(j in c(1:numbofvar)){
assign(modelstate[j],pX[,j],envir=tmp.env)
}
drif.term<-array(0,c(Tbig,numbofvar))
for(i in c(1:numbofvar))
drif.term [,i]<- eval(DRIFT[i],envir=tmp.env)
# Check using variable in the drift
# jump.term<-sapply(1:numbofvar,function(i){
# sapply(1:numbLev, function(j){
# eval(JUMP[[i]][j],envir=tmp.env)
# },simplify = TRUE)
# },simplify = TRUE)
jump.term<-array(0,c(numbofvar,numbLev,Tbig))
for(i in c(1:numbofvar)){
for(j in c(1:numbLev))
jump.term[i,j, ] <- eval(JUMP[[i]][j],envir=tmp.env)
}
# if(dim(jump.term)[1]==numbofvar){
# if(dim(jump.term)[2]==numbofvar){
# if(det(jump.term)==0){
# Invjump.term<-solve(t(jump.term)%*%jump.term)%*%t(jump.term)
# }else{
# Invjump.term<-solve(jump.term)
# }
# }else{
# Invjump.term<-solve(t(jump.term)%*%jump.term)%*%t(jump.term)
# }
# Invjump.term <- Invjump.term%o%rep(1,Tbig)
# }else{
#
# }
#
DeltaInc<-(inc-drif.term*h)
if(dim(jump.term)[1]==numbofvar){
if(dim(jump.term)[2]==numbofvar){
resi<-t(sapply(i:Tbig,function(i){
if(det(jump.term[,,i])==0){
step1<-t(jump.term[,,i])%*%jump.term[,,i]
if(det(step1)==0){
Invjump.term<-diag(rep(1,dim(step1)[1]))
}else{
Invjump.term<-solve(step1)%*%t(jump.term[,,i])
}
}else{
Invjump.term<-solve(jump.term[,,i])
}
Invjump.term%*% DeltaInc[i,]
}
)
)
}else{
resi<-t(sapply(i:Tbig,function(i){
step1<-t(jump.term[,,i])%*%jump.term[,,i]
if(det(step1)==0){
Invjump.term<-diag(rep(1,dim(step1)[1]))
}else{
Invjump.term<-solve(step1)%*%t(jump.term[,,i])
}
Invjump.term%*% DeltaInc[i,]
}
)
)
}
}
if(aggregation){
Ter <- min(floor(yuima@sampling@Terminal))
res.incr<-t(sapply(1:Ter,function(i) colSums(resi[(floor((i-1)/h)):(floor(i/h)-1),]) ))
}else{
res.incr<-resi
}
}
if(aggregation){
if(!is.matrix(res.incr)){
res.incr<- as.matrix(res.incr)
}
if(dim(res.incr)[2]==1){
colnames(res.incr)<-sdeModel@jump.variable
}else{
colnames(res.incr)<-paste0(sdeModel@jump.variable,c(1:dim(res.incr)[2]))
}
Incr.Lev <- zooreg(data=res.incr)
Incr.Lev<- setData(original.data = Incr.Lev)
}else{
Incr.Lev <- zoo(res.incr,order.by=yuima@sampling@grid[[1]][-1])
Incr.Lev <- setData(original.data=Incr.Lev)
}
if(length(oldyuima@data@zoo.data)==1){
mydiff<-oldyuima@model@jump.coeff[[1]]
mydiffDer <-deriv(mydiff,oldyuima@model@parameter@jump)
myenvdiff<- new.env()
if(length(oldyuima@model@parameter@jump)>=1){
for(i in c(1:length(oldyuima@model@parameter@jump))){
assign(value=coef[oldyuima@model@parameter@jump[i]],x=oldyuima@model@parameter@jump[i],envir=myenvdiff)
}
}
EvalPartDiff <- Vectorize(FUN= function(myenvdiff,mydiffDer, data){
assign(x=oldyuima@model@solve.variable, value=data,envir = myenvdiff)
return(attr(eval(mydiffDer, envir=myenvdiff),"gradient"))},vectorize.args = "data")
DiffJumpCoeff<-EvalPartDiff(myenvdiff,mydiffDer, data=pX)
if(!is.matrix(DiffJumpCoeff)){
sigmadiffhat<- as.matrix(sum(DiffJumpCoeff^2/jump.term[1:(oldyuima@sampling@n-1)]^2)/(oldyuima@sampling@n))*coefSigdiff
DiffJumpCoeff<- t(DiffJumpCoeff)
}else{
sigmadiffhat<- matrix(0,dim(DiffJumpCoeff)[1],dim(DiffJumpCoeff)[1])
for(t in c(1:dim(DiffJumpCoeff)[2])){
sigmadiffhat <-sigmadiffhat+as.matrix(DiffJumpCoeff[,t])%*%DiffJumpCoeff[,t]/jump.term[t]^2
}
sigmadiffhat<- sigmadiffhat/(oldyuima@sampling@n)*coefSigdiff
}
mydrift<-oldyuima@model@drift[[1]]
mydriftDer <-deriv(mydrift,oldyuima@model@parameter@drift)
myenvdrift<- new.env()
if(length(oldyuima@model@parameter@drift)>=1){
for(i in c(1:length(oldyuima@model@parameter@drift))){
assign(value=coef[oldyuima@model@parameter@drift[i]],x=oldyuima@model@parameter@drift[i],envir=myenvdrift)
}
}
DriftDerCoeff<-EvalPartDiff(myenvdrift,mydriftDer, data=pX)
if(!is.matrix(DriftDerCoeff)){
# sigmadrifthat<- as.matrix(sum(DriftDerCoeff^2/jump.term[1:(oldyuima@sampling@n-1)]^2)/(oldyuima@sampling@n))*coefDriftSig
sigmadrifthat<- as.matrix(sum(DriftDerCoeff^2/jump.term[1:(oldyuima@sampling@n-1)]^2)/(oldyuima@sampling@n))
DriftDerCoeff <- t(DriftDerCoeff)
}else{
sigmadrifthat<- matrix(0,dim(DriftDerCoeff)[1],dim(DriftDerCoeff)[1])
for(t in c(1:dim(DriftDerCoeff)[2])){
sigmadrifthat <-sigmadrifthat+as.matrix(DriftDerCoeff[,t])%*%DriftDerCoeff[,t]/jump.term[t]^2
}
sigmadrifthat<- sigmadrifthat/(oldyuima@sampling@n)
}
sigmadriftdiff <- matrix(0, dim(sigmadrifthat)[2],dim(sigmadiffhat)[1])
for(t in c(1:dim(DriftDerCoeff)[2]))
sigmadriftdiff<-sigmadriftdiff+DriftDerCoeff[,t]%*%t(DiffJumpCoeff[,t])
#sigmadriftdiff<-sigmadriftdiff/oldyuima@sampling@n
sigmadriftdiff<-sigmadriftdiff/oldyuima@sampling@n*coefDriftSig
MatSigmaHat <- rbind(cbind(sigmadiffhat,t(sigmadriftdiff)),cbind(sigmadriftdiff,sigmadrifthat))
res@coef<-res@coef[c(oldyuima@model@parameter@jump,oldyuima@model@parameter@drift)]
res@vcov<-solve(t(myGamhat)%*%solve(MatSigmaHat)%*%myGamhat*oldyuima@sampling@Terminal)
}
if(Est.Incr == "Incr"){
if(length(oldyuima@data@zoo.data)==1){
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
Data = yuima@data, yuima=res)
}else{
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
Data = yuima@data, yuima=res)
vcovLevyNoMeas <- function(myres, Gammahat0, sq=TRUE){
#myres <- res.VG2
DeltaX <- apply(myres@Data@original.data,2,diff)
myData<- myres@Data@original.data
CmatExpr<- myres@model@jump.coeff
ncolC <-length(myres@model@jump.coeff[[1]])
param <- myres@coef[myres@model@parameter@jump]
aexpr<- myres@model@drift
namedrift<-myres@model@parameter@drift
pardrif <- myres@coef[namedrift]
avect_exp<-myres@model@drift
Jac_Drift <- function(aexpr,namedrift,nobs=length(aexpr)){
lapply(X=c(1:nobs),FUN=function(X,namedrift,aexpr){
return(deriv(aexpr[X],namedrift))
},namedrift=namedrift,aexpr=aexpr)
}
Jac_DriftExp <- Jac_Drift(aexpr=avect_exp,namedrift)
FUNDum<-function(foo,myenv) sapply(foo, function(x,env) eval(x,envir = env), env= myenv)
h<-diff(time(myres@Data@zoo.data[[1]]))[1]
dummyf1n<- function(DeltaX, Cmat, h){
C2<-t(Cmat)%*%Cmat
dec <- chol(C2) # Eventualy Add a tryCatch
tmp <- t(DeltaX)%*%solve(C2)%*%DeltaX
logretval <- -h*sum(log(diag(dec))) - 0.5 * as.numeric(tmp)
return(logretval)
}
dummyInc<- function(DeltaX,Cmat, avect,h,sq=TRUE){
if(sq){
Incr <- solve(Cmat)%*%(DeltaX-avect*h)
}else{
C2<-t(Cmat)%*%Cmat
Incr <- solve(C2)%*%Cmat%*%(DeltaX-avect*h)
}
return(Incr)
}
dummyf2n<- function(DeltaX, avect, Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
tmp <- t(Incr)%*%solve(C2)%*%Incr
logretval <- - 0.5/h * as.numeric(tmp)
return(logretval)
}
dumGrad_f2n<-function(DeltaX, avect, Jac_a,Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
Grad<-t(Jac_a)%*%solve(C2)%*%Incr
return(Grad)
}
f1n_j<-function(x, myObsDelta, CmatExpr,h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef )
return(dummyf1n(DeltaX=myObsDelta, Cmat=Cmat, h=h))
}
Incr_Func <- function(x, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq=TRUE){
names(myData)<-myres@model@solve.variable
newenv <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenv )
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenv)
}
return(dummyInc(DeltaX= myObsDelta,Cmat, avect,h,sq=sq))
}
f2n_j <- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
}
return(dummyf2n(DeltaX=myObsDelta, avect=avect, Cmat=Cmat, h=h))
}
Gradf2n_j <-function(x, parDiff, myObsDelta, CmatExpr,
avect_exp, Jac_DriftExp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
Jac_a<- matrix(0,dd,length(x))
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
Jac_a[j,]<-attr(eval(Jac_DriftExp[[j]],envir=newenvDriftCoef),"gradient")
}
return(dumGrad_f2n(DeltaX=myObsDelta, avect=avect, Jac_a=Jac_a, Cmat=Cmat, h=h))
}
# f1n_j(x=param, myObsDelta=DeltaX[1,], CmatExpr=CmatExpr, h=h)
#i=1
# debug(dummyInc)
# Incr_Func(x=c(param,pardrif), myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, sq=TRUE)
# f1n_j(x=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,], myres=myres)
# f2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, avect_exp=avect_exp,
# h=h, myData=myData[i,], myres=myres)
# Gradf2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
# avect_exp, Jac_DriftExp, h, myData[i,], myres)
del <- 10^-3
dummy <- t(rep(1,length(param)))
myeta<- as.matrix(param)%*%dummy
dummyG <- t(rep(1,length(c(param,pardrif))))
globalmyeta <- as.matrix(c(param,pardrif))%*%dummyG
Incr <- del*diag(rep(1,dim(myeta)[1]))
GlobIncr <- del*diag(rep(1,dim(globalmyeta)[1]))
Sigma_gamma <- matrix(0 ,length(param),length(param))
Sigma_alpha <- matrix(0 ,length(pardrif),length(pardrif))
Sigma_algam <- matrix(0 ,length(pardrif),length(param))
histDeltaf1n_j_delta <-matrix(0 , dim(DeltaX)[1],length(param))
histDeltaf2n_j_delta <- matrix(0 , dim(DeltaX)[1],length(pardrif))
# histb_incr <- array(0, c(dim(DeltaX)[2],dim(DeltaX)[1],length(c(param,pardrif))))
for(i in c(1:dim(DeltaX)[1])){
Deltaf1n_j_delta<-sapply(X=1:dim(myeta)[1],
FUN = function(X,myObsDelta, CmatExpr, h, myData, myres,del){
par1<-myeta[,X]+Incr[,X]
#par[oldyuima@model@measure$df@time.var]<-1
f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
par2<-myeta[,X]-Incr[,X]
f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,],
myres=myres, del=del)
# DeltaInc <- sapply(X=1:dim(GlobIncr)[1],
# FUN = function(X, myObsDelta, CmatExpr,avect_exp, h,
# myData, myres, del, sq){
# par1<-globalmyeta[,X]+GlobIncr[,X]
#
# # f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
# f1<-Incr_Func(x=par1, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
# par2<-globalmyeta[,X]-GlobIncr[,X]
# f2<-Incr_Func(x=par2, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
# #f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
# return((f1-f2)/(2*del))
# },
# myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, del=del,sq=sq
# )
#
# histDeltaf1n_j_delta[i, ]<-Deltaf1n_j_delta
#histb_incr[ , i, ] <- DeltaInc
Sigma_gamma <- Sigma_gamma + as.matrix(Deltaf1n_j_delta)%*%t(Deltaf1n_j_delta)
Deltaf2n_j_delta<- Gradf2n_j(x=pardrif, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
avect_exp, Jac_DriftExp, h, myData[i,], myres)
histDeltaf2n_j_delta[i,]<-Deltaf2n_j_delta
Sigma_alpha <- Sigma_alpha + Deltaf2n_j_delta%*%t(Deltaf2n_j_delta)
Sigma_algam <- Sigma_algam + Deltaf2n_j_delta%*%t(Deltaf1n_j_delta)
#cat("\n",i)
}
Tn<-tail(time(myres@Data@original.data),1L)
Sigma_gamma0<-Sigma_gamma/Tn
Sigma_alpha0 <- Sigma_alpha/Tn
Sigma_algam0 <- Sigma_algam/Tn
Sigma0 <- cbind(rbind(Sigma_gamma0,Sigma_algam0),rbind(t(Sigma_algam0),Sigma_alpha0))
InvGammaHAT <- solve(Gammahat0)
vcov <- InvGammaHAT %*% Sigma0 %*% InvGammaHAT/Tn
myres@vcov<- vcov
return(myres)
}
if(length(result@model@jump.coeff)==length(result@model@jump.coeff[[1]])){
sq<-TRUE
}else{
sq<-FALSE
}
result<-vcovLevyNoMeas(myres=result, Gammahat0=myGamhat, sq=sq)
}
return(result)
}
cat("\nEstimation Levy parameters ... \n")
#if(class(mylaw)=="yuima.law"){
if(inherits(mylaw, "yuima.law")){ # YK, Mar. 22, 2022
if(aggregation){
minusloglik <- function(para){
para[length(para)+1]<-1
names(para)[length(para)]<-yuima@model@time.variable
-sum(dens(object=mylaw, x=res.incr, param = para, log = TRUE),
na.rm = T)
}
}else{
minusloglik <- function(para){
para[length(para)+1] <- yuima@sampling@delta
names(para)[length(para)]<-yuima@model@time.variable
-sum(dens(object=mylaw, x=res.incr, param = para, log = TRUE),
na.rm = T)
}
}
para <- start0[lev.names]
lowerjump <- lower0[lev.names]
upperjump <- upper0[lev.names]
esti <- optim(fn = minusloglik, lower = lowerjump, upper = upperjump,
par = para, method = "L-BFGS-B")
HessianEta <- optimHess(par=esti$par, fn=minusloglik)
res@coef<-c(res@coef,esti$par)
res@fullcoef[names(para)]<-esti$par
if(length(oldyuima@data@zoo.data)==1 & is(oldyuima@model@measure$df, "yuima.law")){
if(!aggregation){
Ter <- yuima@sampling@Terminal
ures <- numeric(floor(Ter))
for(l in 1:floor(Ter)){
ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
}
}
mypar<-res@coef[oldyuima@model@parameter@measure]
mypar[oldyuima@model@measure$df@time.var]<-1
fdataeta<-dens(object=oldyuima@model@measure$df,x=ures,param=mypar)# f(eps, eta)
del <- 10^-3
fdatadeltaeta<- dens(object=oldyuima@model@measure$df,x=ures+del,param=mypar) # f(eps + delta, eta)
dummy <- t(rep(1,length(mypar[oldyuima@model@measure$df@param.measure])))
myeta<- as.matrix(mypar[oldyuima@model@measure$df@param.measure])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[oldyuima@model@measure$df@time.var]<-1
dens(object=oldyuima@model@measure$df,x=ures,param=par)
}
)# f(eps, eta+delta)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[oldyuima@model@measure$df@time.var]<-1
dens(object=oldyuima@model@measure$df,x=ures+del,param=par)
}
) # f(eps +deta, eta+delta)
term1<-1/(fdataeta)
term2 <- fdatadeltaeta*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial<-t((as.matrix(term1)%*%dummy)/del^2*term2/oldyuima@sampling@Terminal)
# construction of b_i
# DiffJumpCoeff, DriftDerCoeff, jump.term length(resi)
# step1 <- t(DiffJumpCoeff)%*%DiffJumpCoeff
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/oldyuima@sampling@Terminal
#SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term[-length(jump.term)]^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha <- SigmaEtaAlpha*sum(resi^3)/oldyuima@sampling@delta
b_i <- matrix(0,floor(Ter),length(c(oldyuima@model@parameter@drift, oldyuima@model@parameter@jump)))
Coef1 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@jump))
Coef2 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@drift))
for(l in 1:floor(Ter)){
pos <- (floor((l-1)/h)):(floor(l/h)-1)
if(length(oldyuima@model@parameter@jump)==1){
b_i[l,1:length(oldyuima@model@parameter@jump)] <- sum(-DiffJumpCoeff[,pos]*resi[pos]/jump.term[pos])
Coef1[l,]<-sum(DiffJumpCoeff[,pos]/jump.term[pos]*(resi[pos]^2-h))
}else{
interm <- as.matrix(resi[pos]/jump.term[pos])
b_i[l,1:length(oldyuima@model@parameter@jump)] <- -t(DiffJumpCoeff[,pos]%*%interm)
interm2 <- as.matrix((resi[pos]^2-h)/jump.term[pos])
Coef1[l,] <-DiffJumpCoeff[,pos]%*%interm2
}
if(length(oldyuima@model@parameter@drift)==1){
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <- -sum(h* DriftDerCoeff[,pos]%*%jump.term[pos])
Coef2[l,]<-sum(DriftDerCoeff[,pos]/jump.term[pos]*(resi[pos]))
}else{
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <--h* DriftDerCoeff[,pos]%*%jump.term[pos]
interm3 <- as.matrix((resi[pos])/jump.term[pos])
Coef2[l,] <-DriftDerCoeff[,pos]%*%interm3
}
}
MatrUnder <- mixpartial%*%b_i
I_n <- cbind(rbind(myGamhat,MatrUnder),rbind(matrix(0, dim(myGamhat)[1],dim(HessianEta)[2]),HessianEta/oldyuima@sampling@Terminal))
SigmaGammaEta <- t(DerMeta)%*%Coef1/Ter
SigmaAlphaEta <- t(DerMeta)%*%Coef2/Ter
# dim(fdataetadelta), length(fdataeta), length(term1)
dum <- cbind(SigmaGammaEta , SigmaAlphaEta)
MatSigmaHat1<- rbind(cbind(MatSigmaHat,t(dum)),cbind(dum,SigmaEta))
InvIn<- solve(I_n)
res@vcov <-InvIn%*%MatSigmaHat1%*%t(InvIn)/Ter
colnames(res@vcov)<-names(res@fullcoef)
#res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
rownames(res@vcov)<-names(res@fullcoef)
res@min<-c(res@min,esti$value)
res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
minusloglLevy = minusloglik,logL.Incr=-esti$value,
Data = yuima@data, yuima=res, Levydetails=esti)
}else{
Tn<-yuima@sampling@Terminal
HessianEta_divTn <- HessianEta/Tn
if(!aggregation){
Ter <- min(floor(yuima@sampling@Terminal))
ures<-t(sapply(1:Ter,function(i) colSums(resi[(floor((i-1)/h)):(floor(i/h)-1),]) ))
#yuima.stop("da fare")
vcovLevy1 <- function(myres, HessianEta_divTn, Gammahat0, ures, sq=TRUE){
#myres <- res.VG2
DeltaX <- apply(myres@Data@original.data,2,diff)
myData<- myres@Data@original.data
CmatExpr<- myres@model@jump.coeff
ncolC <-length(myres@model@jump.coeff[[1]])
param <- myres@coef[myres@model@parameter@jump]
aexpr<- myres@model@drift
namedrift<-myres@model@parameter@drift
pardrif <- myres@coef[namedrift]
avect_exp<-myres@model@drift
Jac_Drift <- function(aexpr,namedrift,nobs=length(aexpr)){
lapply(X=c(1:nobs),FUN=function(X,namedrift,aexpr){
return(deriv(aexpr[X],namedrift))
},namedrift=namedrift,aexpr=aexpr)
}
Jac_DriftExp <- Jac_Drift(aexpr=avect_exp,namedrift)
FUNDum<-function(foo,myenv) sapply(foo, function(x,env) eval(x,envir = env), env= myenv)
h<-diff(time(myres@Data@zoo.data[[1]]))[1]
dummyf1n<- function(DeltaX, Cmat, h){
C2<-t(Cmat)%*%Cmat
dec <- chol(C2) # Eventualy Add a tryCatch
tmp <- t(DeltaX)%*%solve(C2)%*%DeltaX
logretval <- -h*sum(log(diag(dec))) - 0.5 * as.numeric(tmp)
return(logretval)
}
dummyInc<- function(DeltaX,Cmat, avect,h,sq=TRUE){
if(sq){
Incr <- solve(Cmat)%*%(DeltaX-avect*h)
}else{
C2<-t(Cmat)%*%Cmat
Incr <- solve(C2)%*%Cmat%*%(DeltaX-avect*h)
}
return(Incr)
}
dummyf2n<- function(DeltaX, avect, Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
tmp <- t(Incr)%*%solve(C2)%*%Incr
logretval <- - 0.5/h * as.numeric(tmp)
return(logretval)
}
dumGrad_f2n<-function(DeltaX, avect, Jac_a,Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
Grad<-t(Jac_a)%*%solve(C2)%*%Incr
return(Grad)
}
f1n_j<-function(x, myObsDelta, CmatExpr,h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef )
return(dummyf1n(DeltaX=myObsDelta, Cmat=Cmat, h=h))
}
Incr_Func <- function(x, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq=TRUE){
names(myData)<-myres@model@solve.variable
newenv <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenv )
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenv)
}
return(dummyInc(DeltaX= myObsDelta,Cmat, avect,h,sq=sq))
}
f2n_j <- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
}
return(dummyf2n(DeltaX=myObsDelta, avect=avect, Cmat=Cmat, h=h))
}
Gradf2n_j <-function(x, parDiff, myObsDelta, CmatExpr,
avect_exp, Jac_DriftExp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
Jac_a<- matrix(0,dd,length(x))
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
Jac_a[j,]<-attr(eval(Jac_DriftExp[[j]],envir=newenvDriftCoef),"gradient")
}
return(dumGrad_f2n(DeltaX=myObsDelta, avect=avect, Jac_a=Jac_a, Cmat=Cmat, h=h))
}
# f1n_j(x=param, myObsDelta=DeltaX[1,], CmatExpr=CmatExpr, h=h)
#i=1
# debug(dummyInc)
# Incr_Func(x=c(param,pardrif), myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, sq=TRUE)
# f1n_j(x=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,], myres=myres)
# f2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, avect_exp=avect_exp,
# h=h, myData=myData[i,], myres=myres)
# Gradf2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
# avect_exp, Jac_DriftExp, h, myData[i,], myres)
del <- 10^-3
dummy <- t(rep(1,length(param)))
myeta<- as.matrix(param)%*%dummy
dummyG <- t(rep(1,length(c(param,pardrif))))
globalmyeta <- as.matrix(c(param,pardrif))%*%dummyG
Incr <- del*diag(rep(1,dim(myeta)[1]))
GlobIncr <- del*diag(rep(1,dim(globalmyeta)[1]))
Sigma_gamma <- matrix(0 ,length(param),length(param))
Sigma_alpha <- matrix(0 ,length(pardrif),length(pardrif))
Sigma_algam <- matrix(0 ,length(pardrif),length(param))
histDeltaf1n_j_delta <-matrix(0 , dim(DeltaX)[1],length(param))
histDeltaf2n_j_delta <- matrix(0 , dim(DeltaX)[1],length(pardrif))
histb_incr <- array(0, c(dim(DeltaX)[2],dim(DeltaX)[1],length(c(param,pardrif))))
for(i in c(1:dim(DeltaX)[1])){
Deltaf1n_j_delta<-sapply(X=1:dim(myeta)[1],
FUN = function(X,myObsDelta, CmatExpr, h, myData, myres,del){
par1<-myeta[,X]+Incr[,X]
#par[oldyuima@model@measure$df@time.var]<-1
f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
par2<-myeta[,X]-Incr[,X]
f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,],
myres=myres, del=del)
DeltaInc <- sapply(X=1:dim(GlobIncr)[1],
FUN = function(X, myObsDelta, CmatExpr,avect_exp, h,
myData, myres, del, sq){
par1<-globalmyeta[,X]+GlobIncr[,X]
# f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
f1<-Incr_Func(x=par1, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
par2<-globalmyeta[,X]-GlobIncr[,X]
f2<-Incr_Func(x=par2, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
#f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, del=del,sq=sq
)
histDeltaf1n_j_delta[i, ]<-Deltaf1n_j_delta
histb_incr[ , i, ] <- DeltaInc
Sigma_gamma <- Sigma_gamma + as.matrix(Deltaf1n_j_delta)%*%t(Deltaf1n_j_delta)
Deltaf2n_j_delta<- Gradf2n_j(x=pardrif, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
avect_exp, Jac_DriftExp, h, myData[i,], myres)
histDeltaf2n_j_delta[i,]<-Deltaf2n_j_delta
Sigma_alpha <- Sigma_alpha + Deltaf2n_j_delta%*%t(Deltaf2n_j_delta)
Sigma_algam <- Sigma_algam + Deltaf2n_j_delta%*%t(Deltaf1n_j_delta)
#cat("\n",i)
}
Tn<-tail(time(myres@Data@original.data),1L)
Sigma_gamma0<-Sigma_gamma/Tn
Sigma_alpha0 <- Sigma_alpha/Tn
Sigma_algam0 <- Sigma_algam/Tn
Sigma0 <- cbind(rbind(Sigma_gamma0,Sigma_algam0),rbind(t(Sigma_algam0),Sigma_alpha0))
myLogDens <- function(x, myObsDelta, CmatExpr,h,myData, myres, pos){
return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
myLogDens2<- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres, pos){
return(f2n_j(x, parDiff, myObsDelta[pos, ], CmatExpr, avect_exp, h, myData[pos,], myres))
#return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
VectLogDens<-Vectorize(FUN=myLogDens,vectorize.args = "pos")
#VectLogDens2<-Vectorize(FUN=myLogDens2,vectorize.args = "pos")
mylogLik<- function(par,DeltaX,CmatExpr, myData, myres, h, Tn, nobs=dim(DeltaX)[1]){
term<-VectLogDens(x=par,
myObsDelta=DeltaX, CmatExpr=CmatExpr,h=h, myData=myData, myres=myres,pos=c(1:nobs))
return(sum(term)/Tn)
}
mylogLik2<- function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
# term<-VectLogDens2(x=par, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres,
# pos=c(1:nobs))
term<-0
for(j in c(1:nobs)){
term<-term+f2n_j(x=par, parDiff, myObsDelta[j, ], CmatExpr, avect_exp, h, myData[j,], myres)
}
return(term/Tn)
}
GradlogLik2<-function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
term<-matrix(0, length(par),1)
for(j in c(1:nobs)){
term <- term + Gradf2n_j(x=par, parDiff, myObsDelta=myObsDelta[j, ], CmatExpr,
avect_exp, Jac_DriftExp, h, myData=myData[j,], myres)
}
return(as.numeric(term)/Tn)
}
# Gammahat <- optimHess(par=param,fn=mylogLik,
# DeltaX=DeltaX,CmatExpr=CmatExpr,
# h=h, Tn=Tn, nobs=dim(DeltaX)[1],
# myData=myData, myres=myres)
# GammaAlfahat <- optimHess(par=pardrif,fn=mylogLik2,gr=GradlogLik2,
# parDiff=param, myObsDelta=DeltaX,
# CmatExpr=CmatExpr, avect_exp=avect_exp, h=h,
# Tn=Tn, nobs=dim(DeltaX)[1], myData=myData, myres=myres)
#
# Gammahat0 <- cbind(rbind(Gammahat,matrix(0,dim(GammaAlfahat)[1],dim(Gammahat)[2])),
# rbind(matrix(0,dim(Gammahat)[2],dim(GammaAlfahat)[1]),GammaAlfahat))
uhistDeltaf1n_j<- matrix(0,floor(Tn),length(param))
uhistDeltaf2n_j<- matrix(0,floor(Tn),length(pardrif))
aaa<-length(c(param,pardrif))
uhistb_incr <- array(0, c(dim(DeltaX)[2],floor(Tn),aaa))
for(l in 1:floor(Tn)){
#ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
uhistDeltaf1n_j[l, ] <- colSums(histDeltaf1n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
uhistDeltaf2n_j[l, ] <- colSums(histDeltaf2n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
for(i in c(1:aaa)){
dumIn <- histb_incr[,(floor((l-1)/h)):(floor(l/h)-1),i]
uhistb_incr[,l,i]<- rowSums(dumIn)
}
}
nMeaspar<-myres@model@parameter@measure
mypar_meas0 <- myres@coef[nMeaspar]#res@coef[oldyuima@model@parameter@measure]
mypar_meas <- c(mypar_meas0,1)
# ures<-myres@Incr.Lev@original.data
names(mypar_meas)<-c(nMeaspar,myres@model@measure$df@time.var)
fdataeta<-dens(object=myres@model@measure$df,x=ures,param=mypar_meas)# f(eps, eta)
del <- 10^-3
dummy <- t(rep(1,length(mypar_meas[myres@model@measure$df@param.measure])))
myeta<- as.matrix(mypar_meas[myres@model@measure$df@param.measure])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures,param=par)
}
)# f(eps, eta+delta)
term1<-1/(fdataeta)
dummyvecdel<-numeric(length=dim(ures)[2])
fdatadeltaeta<- matrix(0,floor(Tn),dim(ures)[2])
mixpartial <-array(0,c(length(nMeaspar),floor(Tn),dim(ures)[2]))
for(j in c(1:dim(ures)[2])){
dummyvecdel[j]<-del
fdatadeltaeta[,j]<- dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=mypar_meas)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=par)
}
) # f(eps +deta, eta+delta)
dummyvecdel<-numeric(length=dim(ures)[2])
term2 <- fdatadeltaeta[,j]*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial[,,j]<-t((as.matrix(term1)%*%dummy)/del^2*term2/Tn)
}
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/Tn
minusloglik <- function(para){
para[length(para)+1]<-1
names(para)[length(para)]<-myres@model@time.variable
-sum(dens(object=myres@model@measure$df, x=ures, param = para, log = TRUE),
na.rm = T)/Tn
}
# HessianEta_divTn <- optimHess(par=mypar_meas0, fn=minusloglik)
Gammaeta_theta <- matrix(0,length(mypar_meas0), aaa)
for(t in c(1:floor(Tn))){
Gammaeta_theta<-Gammaeta_theta+mixpartial[,t,]%*%uhistb_incr[,t,]
}
GammaEta_Theta<- -1/Tn*Gammaeta_theta
Sigma_eta_theta<-t(DerMeta)%*%cbind(uhistDeltaf1n_j,uhistDeltaf2n_j)/Tn
Sigma <- cbind(rbind(Sigma0,Sigma_eta_theta),rbind(t(Sigma_eta_theta),SigmaEta))
GammaHAT<-cbind(rbind(Gammahat0, GammaEta_Theta), rbind(t(GammaEta_Theta), HessianEta_divTn))
InvGammaHAT <- solve(GammaHAT)
vcov <- InvGammaHAT %*% Sigma %*% InvGammaHAT/Tn
myres@vcov<- vcov
return(myres)
}
}
res@vcov<-cbind(res@vcov,matrix(NA,ncol=length(esti$par),nrow=dim(res@vcov)[1]))
res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
colnames(res@vcov)<-names(res@fullcoef)
#res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
rownames(res@vcov)<-names(res@fullcoef)
res@min<-c(res@min,esti$value)
res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
minusloglLevy = minusloglik,logL.Incr=-esti$value,
Data = yuima@data, yuima=res, Levydetails=esti)
if(length(result@model@jump.coeff)==length(result@model@jump.coeff[[1]])){
sq<-TRUE
}else{
sq<-FALSE
}
if(!aggregation){
result <- vcovLevy1(myres = result, HessianEta_divTn = HessianEta_divTn,
Gammahat0 = myGamhat, ures = ures, sq=TRUE)
}else{
vcovLevy <- function(myres, HessianEta_divTn, Gammahat0, sq=TRUE){
#myres <- res.VG2
DeltaX <- apply(myres@Data@original.data,2,diff)
myData<- myres@Data@original.data
CmatExpr<- myres@model@jump.coeff
ncolC <-length(myres@model@jump.coeff[[1]])
param <- myres@coef[myres@model@parameter@jump]
aexpr<- myres@model@drift
namedrift<-myres@model@parameter@drift
pardrif <- myres@coef[namedrift]
avect_exp<-myres@model@drift
Jac_Drift <- function(aexpr,namedrift,nobs=length(aexpr)){
lapply(X=c(1:nobs),FUN=function(X,namedrift,aexpr){
return(deriv(aexpr[X],namedrift))
},namedrift=namedrift,aexpr=aexpr)
}
Jac_DriftExp <- Jac_Drift(aexpr=avect_exp,namedrift)
FUNDum<-function(foo,myenv) sapply(foo, function(x,env) eval(x,envir = env), env= myenv)
h<-diff(time(myres@Data@zoo.data[[1]]))[1]
dummyf1n<- function(DeltaX, Cmat, h){
C2<-t(Cmat)%*%Cmat
dec <- chol(C2) # Eventualy Add a tryCatch
tmp <- t(DeltaX)%*%solve(C2)%*%DeltaX
logretval <- -h*sum(log(diag(dec))) - 0.5 * as.numeric(tmp)
return(logretval)
}
dummyInc<- function(DeltaX,Cmat, avect,h,sq=TRUE){
if(sq){
Incr <- solve(Cmat)%*%(DeltaX-avect*h)
}else{
C2<-t(Cmat)%*%Cmat
Incr <- solve(C2)%*%Cmat%*%(DeltaX-avect*h)
}
return(Incr)
}
dummyf2n<- function(DeltaX, avect, Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
tmp <- t(Incr)%*%solve(C2)%*%Incr
logretval <- - 0.5/h * as.numeric(tmp)
return(logretval)
}
dumGrad_f2n<-function(DeltaX, avect, Jac_a,Cmat, h){
C2 <- t(Cmat)%*%Cmat
Incr <- DeltaX-h*avect
Grad<-t(Jac_a)%*%solve(C2)%*%Incr
return(Grad)
}
f1n_j<-function(x, myObsDelta, CmatExpr,h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef )
return(dummyf1n(DeltaX=myObsDelta, Cmat=Cmat, h=h))
}
Incr_Func <- function(x, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq=TRUE){
names(myData)<-myres@model@solve.variable
newenv <- list2env(as.list(c(x,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenv )
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenv)
}
return(dummyInc(DeltaX= myObsDelta,Cmat, avect,h,sq=sq))
}
f2n_j <- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
}
return(dummyf2n(DeltaX=myObsDelta, avect=avect, Cmat=Cmat, h=h))
}
Gradf2n_j <-function(x, parDiff, myObsDelta, CmatExpr,
avect_exp, Jac_DriftExp, h, myData, myres){
names(myData)<-myres@model@solve.variable
newenvJumpCoef <- list2env(as.list(c(parDiff,myData)))
Cmat<-sapply(X=CmatExpr, FUN=FUNDum, myenv=newenvJumpCoef)
newenvDriftCoef <- list2env(as.list(c(x,myData)))
dd<-length(avect_exp)
avect<-numeric(length=dd)
Jac_a<- matrix(0,dd,length(x))
for(j in c(1:dd)){
avect[j]<-eval(avect_exp[j],envir=newenvDriftCoef)
Jac_a[j,]<-attr(eval(Jac_DriftExp[[j]],envir=newenvDriftCoef),"gradient")
}
return(dumGrad_f2n(DeltaX=myObsDelta, avect=avect, Jac_a=Jac_a, Cmat=Cmat, h=h))
}
# f1n_j(x=param, myObsDelta=DeltaX[1,], CmatExpr=CmatExpr, h=h)
#i=1
# debug(dummyInc)
# Incr_Func(x=c(param,pardrif), myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, sq=TRUE)
# f1n_j(x=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,], myres=myres)
# f2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, avect_exp=avect_exp,
# h=h, myData=myData[i,], myres=myres)
# Gradf2n_j(x, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
# avect_exp, Jac_DriftExp, h, myData[i,], myres)
del <- 10^-3
dummy <- t(rep(1,length(param)))
myeta<- as.matrix(param)%*%dummy
dummyG <- t(rep(1,length(c(param,pardrif))))
globalmyeta <- as.matrix(c(param,pardrif))%*%dummyG
Incr <- del*diag(rep(1,dim(myeta)[1]))
GlobIncr <- del*diag(rep(1,dim(globalmyeta)[1]))
Sigma_gamma <- matrix(0 ,length(param),length(param))
Sigma_alpha <- matrix(0 ,length(pardrif),length(pardrif))
Sigma_algam <- matrix(0 ,length(pardrif),length(param))
histDeltaf1n_j_delta <-matrix(0 , dim(DeltaX)[1],length(param))
histDeltaf2n_j_delta <- matrix(0 , dim(DeltaX)[1],length(pardrif))
histb_incr <- array(0, c(dim(DeltaX)[2],dim(DeltaX)[1],length(c(param,pardrif))))
for(i in c(1:dim(DeltaX)[1])){
Deltaf1n_j_delta<-sapply(X=1:dim(myeta)[1],
FUN = function(X,myObsDelta, CmatExpr, h, myData, myres,del){
par1<-myeta[,X]+Incr[,X]
#par[oldyuima@model@measure$df@time.var]<-1
f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
par2<-myeta[,X]-Incr[,X]
f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr=CmatExpr, h=h, myData=myData[i,],
myres=myres, del=del)
DeltaInc <- sapply(X=1:dim(GlobIncr)[1],
FUN = function(X, myObsDelta, CmatExpr,avect_exp, h,
myData, myres, del, sq){
par1<-globalmyeta[,X]+GlobIncr[,X]
# f1<-f1n_j(x=par1, myObsDelta, CmatExpr, h, myData, myres)
f1<-Incr_Func(x=par1, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
par2<-globalmyeta[,X]-GlobIncr[,X]
f2<-Incr_Func(x=par2, myObsDelta, CmatExpr,avect_exp, h, myData, myres, sq)
#f2<-f1n_j(x=par2, myObsDelta, CmatExpr, h, myData, myres)
return((f1-f2)/(2*del))
},
myObsDelta=DeltaX[i,], CmatExpr,avect_exp, h, myData=myData[i,], myres, del=del,sq=sq
)
histDeltaf1n_j_delta[i, ]<-Deltaf1n_j_delta
histb_incr[ , i, ] <- DeltaInc
Sigma_gamma <- Sigma_gamma + as.matrix(Deltaf1n_j_delta)%*%t(Deltaf1n_j_delta)
Deltaf2n_j_delta<- Gradf2n_j(x=pardrif, parDiff=param, myObsDelta=DeltaX[i,], CmatExpr,
avect_exp, Jac_DriftExp, h, myData[i,], myres)
histDeltaf2n_j_delta[i,]<-Deltaf2n_j_delta
Sigma_alpha <- Sigma_alpha + Deltaf2n_j_delta%*%t(Deltaf2n_j_delta)
Sigma_algam <- Sigma_algam + Deltaf2n_j_delta%*%t(Deltaf1n_j_delta)
#cat("\n",i)
}
Tn<-tail(time(myres@Data@original.data),1L)
Sigma_gamma0<-Sigma_gamma/Tn
Sigma_alpha0 <- Sigma_alpha/Tn
Sigma_algam0 <- Sigma_algam/Tn
Sigma0 <- cbind(rbind(Sigma_gamma0,Sigma_algam0),rbind(t(Sigma_algam0),Sigma_alpha0))
myLogDens <- function(x, myObsDelta, CmatExpr,h,myData, myres, pos){
return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
myLogDens2<- function(x, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres, pos){
return(f2n_j(x, parDiff, myObsDelta[pos, ], CmatExpr, avect_exp, h, myData[pos,], myres))
#return(f1n_j(x, myObsDelta[pos, ], CmatExpr,h,myData=myData[pos,], myres=myres))
}
VectLogDens<-Vectorize(FUN=myLogDens,vectorize.args = "pos")
#VectLogDens2<-Vectorize(FUN=myLogDens2,vectorize.args = "pos")
mylogLik<- function(par,DeltaX,CmatExpr, myData, myres, h, Tn, nobs=dim(DeltaX)[1]){
term<-VectLogDens(x=par,
myObsDelta=DeltaX, CmatExpr=CmatExpr,h=h, myData=myData, myres=myres,pos=c(1:nobs))
return(sum(term)/Tn)
}
mylogLik2<- function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
# term<-VectLogDens2(x=par, parDiff, myObsDelta, CmatExpr, avect_exp, h, myData, myres,
# pos=c(1:nobs))
term<-0
for(j in c(1:nobs)){
term<-term+f2n_j(x=par, parDiff, myObsDelta[j, ], CmatExpr, avect_exp, h, myData[j,], myres)
}
return(term/Tn)
}
GradlogLik2<-function(par, parDiff, myObsDelta, CmatExpr, avect_exp, h, Tn, myData, myres, nobs=dim(DeltaX)[1]){
term<-matrix(0, length(par),1)
for(j in c(1:nobs)){
term <- term + Gradf2n_j(x=par, parDiff, myObsDelta=myObsDelta[j, ], CmatExpr,
avect_exp, Jac_DriftExp, h, myData=myData[j,], myres)
}
return(as.numeric(term)/Tn)
}
# Gammahat <- optimHess(par=param,fn=mylogLik,
# DeltaX=DeltaX,CmatExpr=CmatExpr,
# h=h, Tn=Tn, nobs=dim(DeltaX)[1],
# myData=myData, myres=myres)
# GammaAlfahat <- optimHess(par=pardrif,fn=mylogLik2,gr=GradlogLik2,
# parDiff=param, myObsDelta=DeltaX,
# CmatExpr=CmatExpr, avect_exp=avect_exp, h=h,
# Tn=Tn, nobs=dim(DeltaX)[1], myData=myData, myres=myres)
#
# Gammahat0 <- cbind(rbind(Gammahat,matrix(0,dim(GammaAlfahat)[1],dim(Gammahat)[2])),
# rbind(matrix(0,dim(Gammahat)[2],dim(GammaAlfahat)[1]),GammaAlfahat))
uhistDeltaf1n_j<- matrix(0,floor(Tn),length(param))
uhistDeltaf2n_j<- matrix(0,floor(Tn),length(pardrif))
aaa<-length(c(param,pardrif))
uhistb_incr <- array(0, c(dim(DeltaX)[2],floor(Tn),aaa))
for(l in 1:floor(Tn)){
#ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
uhistDeltaf1n_j[l, ] <- colSums(histDeltaf1n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
uhistDeltaf2n_j[l, ] <- colSums(histDeltaf2n_j_delta[(floor((l-1)/h)):(floor(l/h)-1),])
for(i in c(1:aaa)){
dumIn <- histb_incr[,(floor((l-1)/h)):(floor(l/h)-1),i]
uhistb_incr[,l,i]<- rowSums(dumIn)
}
}
nMeaspar<-myres@model@parameter@measure
mypar_meas0 <- myres@coef[nMeaspar]#res@coef[oldyuima@model@parameter@measure]
mypar_meas <- c(mypar_meas0,1)
ures<-myres@Incr.Lev@original.data
names(mypar_meas)<-c(nMeaspar,myres@model@measure$df@time.var)
fdataeta<-dens(object=myres@model@measure$df,x=ures,param=mypar_meas)# f(eps, eta)
del <- 10^-3
dummy <- t(rep(1,length(mypar_meas[myres@model@measure$df@param.measure])))
myeta<- as.matrix(mypar_meas[myres@model@measure$df@param.measure])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures,param=par)
}
)# f(eps, eta+delta)
term1<-1/(fdataeta)
dummyvecdel<-numeric(length=dim(ures)[2])
fdatadeltaeta<- matrix(0,floor(Tn),dim(ures)[2])
mixpartial <-array(0,c(length(nMeaspar),floor(Tn),dim(ures)[2]))
for(j in c(1:dim(ures)[2])){
dummyvecdel[j]<-del
fdatadeltaeta[,j]<- dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=mypar_meas)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
par[myres@model@measure$df@time.var]<-1
dens(object=myres@model@measure$df,x=ures+rep(1,dim(ures)[1])%*%t(dummyvecdel),param=par)
}
) # f(eps +deta, eta+delta)
dummyvecdel<-numeric(length=dim(ures)[2])
term2 <- fdatadeltaeta[,j]*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial[,,j]<-t((as.matrix(term1)%*%dummy)/del^2*term2/Tn)
}
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/Tn
minusloglik <- function(para){
para[length(para)+1]<-1
names(para)[length(para)]<-myres@model@time.variable
-sum(dens(object=myres@model@measure$df, x=ures, param = para, log = TRUE),
na.rm = T)/Tn
}
# HessianEta_divTn <- optimHess(par=mypar_meas0, fn=minusloglik)
Gammaeta_theta <- matrix(0,length(mypar_meas0), aaa)
for(t in c(1:floor(Tn))){
Gammaeta_theta<-Gammaeta_theta+mixpartial[,t,]%*%uhistb_incr[,t,]
}
GammaEta_Theta<- -1/Tn*Gammaeta_theta
Sigma_eta_theta<-t(DerMeta)%*%cbind(uhistDeltaf1n_j,uhistDeltaf2n_j)/Tn
Sigma <- cbind(rbind(Sigma0,Sigma_eta_theta),rbind(t(Sigma_eta_theta),SigmaEta))
GammaHAT<-cbind(rbind(Gammahat0, GammaEta_Theta), rbind(t(GammaEta_Theta), HessianEta_divTn))
InvGammaHAT <- solve(GammaHAT)
vcov <- InvGammaHAT %*% Sigma %*% InvGammaHAT/Tn
myres@vcov<- vcov
return(myres)
}
result <- vcovLevy(result,HessianEta_divTn,myGamhat,sq=sq)
}
#result <- vcovLevy(result,HessianEta_divTn,myGamhat,sq=sq)
# colnames(result@vcov)<-names(res@fullcoef)
# rownames(result@vcov)<-names(res@fullcoef)
}
# colnames(res@vcov)<-names(res@fullcoef)
# #res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
# rownames(res@vcov)<-names(res@fullcoef)
# res@min<-c(res@min,esti$value)
# res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
return(result)
}else{
dist <- substr(as.character(orig.mylaw$df$expr), 2, 10^3)
startjump <- start0[lev.names]
lowerjump <- lower0[lev.names]
upperjump <- upper0[lev.names]
if(length(startjump) == -1){
logdens <- function(para){
exlogdens <- parse(text = sprintf("log(d%s)", dist))
assign(myjumpname, ures, envir = tmp.env)
assign(mymeasureparam, para, envir = tmp.env)
sum(eval(exlogdens, envir = tmp.env))
}
mydens <-function(para){
exdens <- parse(text = sprintf("d%s", dist))
assign(myjumpname, ures, envir = tmp.env)
assign(mymeasureparam, para, envir = tmp.env)
eval(exdens, envir = tmp.env)
}
intervaljump <- c(lowerjump[[1]], upperjump[[1]])
esti <- optimize(logdens, interval = intervaljump, maximum = TRUE)
return(list(sde=esort, meas=esti$maximum))
}else{
logdens <- function(para){
exlogdens <- parse(text = sprintf("log(d%s)", dist))
assign(oldyuima@model@jump.variable, ures, envir = tmp.env)
for(i in c(1:length(oldyuima@model@parameter@measure)))
assign(oldyuima@model@parameter@measure[i], para[[oldyuima@model@parameter@measure[i]]], envir = tmp.env)
-sum(eval(exlogdens, envir = tmp.env),na.rm = T)
}
mydens1 <-function(par,x){
exdens <- parse(text = sprintf("d%s", dist))
assign(myjumpname, x, envir = tmp.env)
assign(mymeasureparam, par, envir = tmp.env)
eval(exdens, envir = tmp.env)
}
esti <- optim(fn=logdens, lower = lowerjump, upper = upperjump, par = startjump,
method = "L-BFGS-B")
HessianEta <- optimHess(par=esti$par, fn=logdens)
res@coef<-c(res@coef,esti$par)
res@fullcoef[lev.names]<-esti$par
if(length(oldyuima@data@zoo.data)==1){
if(!aggregation){
Ter <- yuima@sampling@Terminal
ures <- numeric(floor(Ter))
for(l in 1:floor(Ter)){
ures[l] <- sum(resi[(floor((l-1)/h)):(floor(l/h)-1)])
}
}
mypar<-res@coef[oldyuima@model@parameter@measure]
#mypar[oldyuima@model@measure$df@time.var]<-1
fdataeta<-mydens1(par=mypar,x=ures)# f(eps, eta)
del <- 10^-3
fdatadeltaeta<- mydens1(par=mypar,x=ures+del) # f(eps + delta, eta)
dummy <- t(rep(1,length(mypar[lev.names])))
myeta<- as.matrix(mypar[lev.names])%*%dummy
myetapert <- myeta+del*diag(rep(1,dim(myeta)[1]))
fdataetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
#par[oldyuima@model@measure$df@time.var]<-1
mydens1(par=par,x=ures)
}
)# f(eps, eta+delta)
fdatadeltaetadelta<-sapply(X=1:dim(myeta)[1],FUN = function(X){
par<-myetapert[,X]
#par[oldyuima@model@measure$df@time.var]<-1
mydens1(par=par,x=ures+del)
}
) # f(eps +deta, eta+delta)
term1<-1/(fdataeta)
term2 <- fdatadeltaeta*term1%*%dummy
term2 <- fdatadeltaetadelta-term2*fdataetadelta
mixpartial<-t((as.matrix(term1)%*%dummy)/del^2*term2/oldyuima@sampling@Terminal)
# construction of b_i
# DiffJumpCoeff, DriftDerCoeff, jump.term length(resi)
# step1 <- t(DiffJumpCoeff)%*%DiffJumpCoeff
DerMeta <- 1/del*(fdataetadelta - as.matrix(fdataeta)%*%rep(1,dim(fdataetadelta)[2]))*(as.matrix(term1)%*%rep(1,dim(fdataetadelta)[2]))
SigmaEta <- t(DerMeta)%*%DerMeta/oldyuima@sampling@Terminal
#SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term[-length(jump.term)]^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha<- 1/oldyuima@sampling@n*DriftDerCoeff%*%(t(DiffJumpCoeff)/(as.matrix(jump.term^2)%*%rep(1,dim(DiffJumpCoeff)[1])) )
SigmaEtaAlpha <- SigmaEtaAlpha*sum(resi^3)/oldyuima@sampling@delta
b_i <- matrix(0,floor(Ter),length(c(oldyuima@model@parameter@drift, oldyuima@model@parameter@jump)))
Coef1 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@jump))
Coef2 <- matrix(0,floor(Ter),length( oldyuima@model@parameter@drift))
for(l in 1:floor(Ter)){
pos <- (floor((l-1)/h)):(floor(l/h)-1)
if(length(oldyuima@model@parameter@jump)==1){
b_i[l,1:length(oldyuima@model@parameter@jump)] <- sum(-DiffJumpCoeff[,pos]*resi[pos]/jump.term[pos])
Coef1[l,]<-sum(DiffJumpCoeff[,pos]/jump.term[pos]*(resi[pos]^2-h))
}else{
interm <- as.matrix(resi[pos]/jump.term[pos])
b_i[l,1:length(oldyuima@model@parameter@jump)] <- -t(DiffJumpCoeff[,pos]%*%interm)
interm2 <- as.matrix((resi[pos]^2-h)/jump.term[pos])
Coef1[l,] <-DiffJumpCoeff[,pos]%*%interm2
}
if(length(oldyuima@model@parameter@drift)==1){
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <- -sum(h* DriftDerCoeff[,pos]%*%jump.term[pos])
Coef2[l,]<-sum(DriftDerCoeff[,pos]/jump.term[pos]*(resi[pos]))
}else{
b_i[l,1:length(oldyuima@model@parameter@drift)+length(oldyuima@model@parameter@jump)] <--h* DriftDerCoeff[,pos]%*%jump.term[pos]
interm3 <- as.matrix((resi[pos])/jump.term[pos])
Coef2[l,] <-DriftDerCoeff[,pos]%*%interm3
}
}
MatrUnder <- mixpartial%*%b_i
I_n <- cbind(rbind(myGamhat,MatrUnder),rbind(matrix(0, dim(myGamhat)[1],dim(HessianEta)[2]),HessianEta/oldyuima@sampling@Terminal))
SigmaGammaEta <- t(DerMeta)%*%Coef1/Ter
SigmaAlphaEta <- t(DerMeta)%*%Coef2/Ter
# dim(fdataetadelta), length(fdataeta), length(term1)
dum <- cbind(SigmaGammaEta , SigmaAlphaEta)
MatSigmaHat1<- rbind(cbind(MatSigmaHat,t(dum)),cbind(dum,SigmaEta))
InvIn<- solve(I_n)
res@vcov <-InvIn%*%MatSigmaHat1%*%t(InvIn)/Ter
}else{
res@vcov<-cbind(res@vcov,matrix(NA,ncol=length(esti$par),nrow=dim(res@vcov)[1]))
}
colnames(res@vcov)<-names(res@fullcoef)
#res@vcov<-rbind(res@vcov,matrix(NA,nrow=length(esti$par),ncol=dim(res@vcov)[2]))
rownames(res@vcov)<-names(res@fullcoef)
res@min<-c(res@min,esti$value)
res@nobs<-c(res@nobs,length(Incr.Lev@zoo.data[[1]]))
result<- new("yuima.qmleLevy.incr",Incr.Lev=Incr.Lev,
minusloglLevy = logdens,logL.Incr=-esti$value,
Data = yuima@data, yuima=res, Levydetails=esti)
return(result)
#return(list(sde=esort, meas=esti$par))
}
}
}
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