Nothing
R/llag.R
In yuima: The YUIMA Project Package for SDEs
Defines functions
plot.yuima.llag
print.yuima.llag
llag.avar
make.grid
#lead-lag estimation
#x:data
#setGeneric( "llag", function(x,verbose=FALSE) standardGeneric("llag") )
#setMethod( "llag", "yuima", function(x,verbose=FALSE) llag(x@data,verbose=verbose ))
#setMethod( "llag", "yuima.data", function(x,verbose=FALSE) {
#setGeneric( "llag",
# function(x,from=FALSE,to=FALSE,division=FALSE,verbose=FALSE)
# standardGeneric("llag") )
#setMethod( "llag", "yuima",
# function(x,from=FALSE,to=FALSE,division=FALSE,verbose=FALSE)
# llag(x@data,from=FALSE,to=FALSE,division=FALSE,verbose=verbose ))
#setMethod( "llag", "yuima.data", function(x,from=FALSE,to=FALSE,division=FALSE,verbose=FALSE) {
## function to make the grid if it is missing
make.grid <- function(d, d.size, x, from, to, division){
out <- vector(d.size, mode = "list")
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) == 1){
division <- rep(division,d.size)
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- as.numeric(time(x[[i]]))
time2 <- as.numeric(time(x[[j]]))
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(time1),length(time2)))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- time2[1]-time1[1] # time lag (sec)
num1 <- time1[length(time1)]-time1[1] # elapsed time for series 1
num2 <- time2[length(time2)]-time2[1] # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
out[[num]] <- seq(-num2-tmptheta,num1-tmptheta,length=n)[2:(n-1)]
}
}
return(out)
}
## function to compute asymptotic variances
llag.avar <- function(x, grid, bw, alpha, fisher, ser.diffX, ser.times, vol, cormat, ccor, idx, G, d, d.size, tol){
# treatment of the bandwidth
if(missing(bw)){
bw <- matrix(0, d, d)
for(i in 1:(d - 1)){
for(j in (i + 1):d){
Init <- min(ser.times[[i]][1], ser.times[[j]][1])
Term <- max(tail(ser.times[[i]], n = 1), tail(ser.times[[j]], n = 1))
bw[i, j] <- (Term - Init) * min(length(ser.times[[i]]), length(ser.times[[j]]))^(-0.45)
bw[j, i] <- bw[i, j]
}
}
}else{
bw <- bw/tol
}
bw <- matrix(bw, d, d)
p <- diag(d) # p-values
avar <- vector(d.size,mode="list") # asymptotic variances
CI <- vector(d.size,mode="list") # confidence intervals
names(avar) <- names(ccor)
names(CI) <- names(ccor)
vv <- (2/3) * sapply(ser.diffX, FUN = function(x) sum(x^4)) # AVAR for RV
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
## computing conficence intervals
N.max <- max(length(time1), length(time2))
tmp <- rev(as.numeric(ccor[[num]]))
d1 <- -0.5 * tmp * sqrt(vol[j]/vol[i])
d2 <- -0.5 * tmp * sqrt(vol[i]/vol[j])
avar.tmp <- .C("hycrossavar",
as.double(G[[num]]),
as.double(time1),
as.double(time2),
as.integer(length(G[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(x[[i]]),
as.double(x[[j]]),
as.integer(N.max),
as.double(bw[i, j]),
as.double(vv[i]),
as.double(vv[j]),
as.double(d1^2),
as.double(d2^2),
as.double(2 * d1),
as.double(2 * d2),
as.double(2 * d1 * d2),
covar = double(length(G[[num]])),
corr = double(length(G[[num]])),
PACKAGE = "yuima")$corr / (vol[i] * vol[j])
#avar[[num]][avar[[num]] <= 0] <- NA
if(fisher == TRUE){
z <- atanh(tmp) # the Fisher z transformation of the estimated correlation
se.z <- sqrt(avar.tmp)/(1 - tmp^2)
p[i,j] <- pchisq((atanh(cormat[i,j])/se.z[idx[num]])^2, df=1, lower.tail=FALSE)
CI[[num]] <- zoo(tanh(qnorm(1 - alpha/2) * se.z), -grid[[num]])
}else{
p[i,j] <- pchisq(cormat[i,j]^2/avar.tmp[idx[num]], df=1, lower.tail=FALSE)
c.alpha <- sqrt(qchisq(alpha, df=1, lower.tail = FALSE) * avar.tmp)
CI[[num]] <- zoo(c.alpha, -grid[[num]])
}
p[j,i] <- p[i,j]
avar[[num]] <- zoo(avar.tmp, -grid[[num]])
}
}
return(list(p = p, avar = avar, CI = CI))
}
## main body
setGeneric( "llag", function(x, from = -Inf, to = Inf, division = FALSE,
verbose = (ci || ccor), grid, psd = TRUE, plot = ci,
ccor = ci, ci = FALSE, alpha = 0.01, fisher = TRUE, bw, tol = 1e-6) standardGeneric("llag") )
## yuima-method
setMethod("llag", "yuima", function(x, from, to, division, verbose, grid, psd, plot,
ccor, ci, alpha, fisher, bw, tol)
llag(x@data, from, to, division, verbose, grid, psd, plot, ccor, ci, alpha, fisher, bw, tol))
## yuima.data-method
setMethod("llag", "yuima.data", function(x, from, to, division, verbose, grid, psd, plot,
ccor, ci, alpha, fisher, bw, tol)
llag(x@zoo.data, from, to, division, verbose, grid, psd, plot, ccor, ci, alpha, fisher, bw, tol))
## list-method
setMethod("llag", "list", function(x, from, to, division, verbose, grid, psd, plot,
ccor, ci, alpha, fisher, bw, tol) {
d <- length(x)
d.size <- d*(d-1)/2
# allocate memory
ser.times <- vector(d, mode="list") # time index in 'x'
ser.diffX <- vector(d, mode="list") # difference of data
vol <- double(d)
# treatment of the grid (2016-07-04: we implement this before the NA treatment)
if(missing(grid))
grid <- make.grid(d, d.size, x, from, to, division)
# Set the tolerance to avoid numerical erros in comparison
#tol <- 1e-6
for(i in 1:d){
# NA data must be skipped
idt <- which(is.na(x[[i]]))
if(length(idt>0)){
x[[i]] <- x[[i]][-idt]
}
if(length(x[[i]])<2) {
stop("length of data (w/o NA) must be more than 1")
}
# set data and time index
ser.times[[i]] <- as.numeric(time(x[[i]]))/tol
# set difference of the data
ser.diffX[[i]] <- diff( as.numeric(x[[i]]) )
vol[i] <- sum(ser.diffX[[i]]^2)
}
theta <- matrix(0,d,d)
#d.size <- d*(d-1)/2
crosscor <- vector(d.size,mode="list")
idx <- integer(d.size)
# treatment of the grid
#if(missing(grid))
# grid <- make.grid(d, d.size, x, from, to, division)
if(is.list(grid)){
G <- relist(unlist(grid)/tol, grid)
}else{
if(is.numeric(grid)){
G <- data.frame(matrix(grid/tol,length(grid),d.size))
grid <- data.frame(matrix(grid,length(grid),d.size))
}else{
print("llag:invalid grid")
return(NULL)
}
}
# core part
if(psd){ # positive semidefinite correction is implemented
cormat <- diag(d)
LLR <- diag(d)
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
names(crosscor)[num] <- paste("(",i,",",j,")", sep = "")
tmp <- .C("HYcrosscorr2",
as.integer(length(G[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(G[[num]]),
as.double(time1),
as.double(time2),
#double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
as.double(vol[i]),
as.double(vol[j]),
value=double(length(G[[num]])),
PACKAGE = "yuima")$value
idx[num] <- which.max(abs(tmp))
mlag <- -grid[[num]][idx[num]] # make the first timing of max or min
cor <- tmp[idx[num]]
theta[i,j] <- mlag
cormat[i,j] <- cor
theta[j,i] <- -mlag
cormat[j,i] <- cormat[i,j]
LLR[i,j] <- sum(tmp[grid[[num]] < 0]^2)/sum(tmp[grid[[num]] > 0]^2)
LLR[j,i] <- 1/LLR[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])
}
}
covmat <- diag(sqrt(vol))%*%cormat%*%diag(sqrt(vol))
}else{# non-psd
covmat <- diag(vol)
LLR <- diag(d)
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
names(crosscor)[num] <- paste("(",i,",",j,")", sep = "")
tmp <- .C("HYcrosscov2",
as.integer(length(G[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(G[[num]]),
as.double(time1),
as.double(time2),
#double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
value=double(length(G[[num]])),
PACKAGE = "yuima")$value
idx[num] <- which.max(abs(tmp))
mlag <- -grid[[num]][idx[num]] # make the first timing of max or min
cov <- tmp[idx[num]]
theta[i,j] <- mlag
covmat[i,j] <- cov
theta[j,i] <- -mlag
covmat[j,i] <- covmat[i,j]
LLR[i,j] <- sum(tmp[grid[[num]] < 0]^2)/sum(tmp[grid[[num]] > 0]^2)
LLR[j,i] <- 1/LLR[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])/sqrt(vol[i]*vol[j])
}
}
cormat <- diag(1/sqrt(diag(covmat)))%*%covmat%*%diag(1/sqrt(diag(covmat)))
}
if(ci){ # computing confidence intervals
out <- llag.avar(x = x, grid = grid, bw = bw, alpha = alpha, fisher = fisher,
ser.diffX = ser.diffX, ser.times = ser.times,
vol = vol, cormat = cormat, ccor = crosscor, idx = idx,
G = G, d = d, d.size = d.size, tol = tol)
p <- out$p
CI <- out$CI
avar <- out$avar
colnames(theta) <- names(x)
rownames(theta) <- names(x)
colnames(p) <- names(x)
rownames(p) <- names(x)
if(plot){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
y.max <- max(abs(as.numeric(crosscor[[num]])),as.numeric(CI[[num]]))
plot(crosscor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=expression(theta),ylab=expression(U(theta)),
ylim=c(-y.max,y.max))
lines(CI[[num]],lty=2,col="blue")
lines(-CI[[num]],lty=2,col="blue")
}
}
}
if(verbose==TRUE){
colnames(covmat) <- names(x)
rownames(covmat) <- names(x)
colnames(cormat) <- names(x)
rownames(cormat) <- names(x)
colnames(LLR) <- names(x)
rownames(LLR) <- names(x)
if(ccor){
result <- list(lagcce=theta,p.values=p,covmat=covmat,cormat=cormat,LLR=LLR,ccor=crosscor,avar=avar)
}else{
result <- list(lagcce=theta,p.values=p,covmat=covmat,cormat=cormat,LLR=LLR)
}
}else{
return(theta)
}
}else{
colnames(theta) <- names(x)
rownames(theta) <- names(x)
if(plot){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
plot(crosscor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=expression(theta),ylab=expression(U(theta)))
}
}
}
if(verbose==TRUE){
colnames(covmat) <- names(x)
rownames(covmat) <- names(x)
colnames(cormat) <- names(x)
rownames(cormat) <- names(x)
colnames(LLR) <- names(x)
rownames(LLR) <- names(x)
if(ccor){
result <- list(lagcce=theta,covmat=covmat,cormat=cormat,LLR=LLR,ccor=crosscor)
}else{
result <- list(lagcce=theta,covmat=covmat,cormat=cormat,LLR=LLR)
}
}else{
return(theta)
}
}
class(result) <- "yuima.llag"
return(result)
})
# print method for yuima.llag-class
print.yuima.llag <- function(x, ...){
if(is.null(x$p.values)){
cat("Estimated lead-lag parameters\n")
print(x$lagcce, ...)
cat("Corresponding covariance matrix\n")
print(x$covmat, ...)
cat("Corresponding correlation matrix\n")
print(x$cormat, ...)
cat("Lead-lag ratio\n")
print(x$LLR, ...)
}else{
cat("Estimated lead-lag parameters\n")
print(x$lagcce, ...)
cat("Corresponding p-values\n")
print(x$p.values, ...)
cat("Corresponding covariance matrix\n")
print(x$covmat, ...)
cat("Corresponding correlation matrix\n")
print(x$cormat, ...)
cat("Lead-lag ratio\n")
print(x$LLR, ...)
}
}
# plot method for yuima.llag-class
plot.yuima.llag <- function(x, alpha = 0.01, fisher = TRUE,
main = NULL, xlab = NULL, ylab = NULL, ...){
if(is.null(x$ccor)){
warning("cross-correlation functions were not returned by llag. Set verbose = TRUE and ccor = TRUE to return them.",
call. = FALSE)
return(NULL)
}else{
if(is.null(xlab)) xlab <- expression(theta)
if(is.null(ylab)) ylab <- expression(U(theta))
d <- nrow(x$LLR)
if(is.null(x$avar)){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(is.null(main)){
plot(x$ccor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=xlab,ylab=ylab)
}else{
plot(x$ccor[[num]],main=main,xlab=xlab,ylab=ylab)
}
}
}
}else{
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
G <- time(x$ccor[[num]])
if(fisher == TRUE){
z <- atanh(x$ccor[[num]]) # the Fisher z transformation of the estimated correlation
se.z <- sqrt(x$avar[[num]])/(1 - x$ccor[[num]]^2)
CI <- zoo(tanh(qnorm(1 - alpha/2) * se.z), G)
}else{
c.alpha <- sqrt(qchisq(alpha, df=1, lower.tail = FALSE) * x$avar[[num]])
CI <- zoo(c.alpha, G)
}
y.max <- max(abs(as.numeric(x$ccor[[num]])),as.numeric(CI))
if(is.null(main)){
plot(x$ccor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=xlab,ylab=ylab,ylim=c(-y.max,y.max))
}else{
plot(x$ccor[[num]],main = main,xlab=xlab,ylab=ylab,
ylim=c(-y.max,y.max))
}
lines(CI,lty=2,col="blue")
lines(-CI,lty=2,col="blue")
}
}
}
}
}
## Old version until Oct. 10, 2015
if(0){
setGeneric( "llag",
function(x,from=-Inf,to=Inf,division=FALSE,verbose=FALSE,grid,psd=TRUE,
plot=FALSE,ccor=FALSE)
standardGeneric("llag") )
setMethod( "llag", "yuima",
function(x,from=-Inf,to=Inf,division=FALSE,verbose=FALSE,grid,psd=TRUE,
plot=FALSE,ccor=FALSE)
llag(x@data,from=from,to=to,division=division,verbose=verbose,grid=grid,
psd=psd,plot=plot))
setMethod( "llag", "yuima.data", function(x,from=-Inf,to=Inf,division=FALSE,
verbose=FALSE,grid,psd=TRUE,
plot=FALSE,ccor=FALSE) {
if((is(x)=="yuima")||(is(x)=="yuima.data")){
zdata <- get.zoo.data(x)
}else{
print("llag:invalid argument")
return(NULL)
}
d <- length(zdata)
# allocate memory
ser.times <- vector(d, mode="list") # time index in 'x'
ser.diffX <- vector(d, mode="list") # difference of data
vol <- double(d)
# Set the tolerance to avoid numerical erros in comparison
tol <- 1e-6
for(i in 1:d){
# NA data must be skipped
idt <- which(is.na(zdata[[i]]))
if(length(idt>0)){
zdata[[i]] <- zdata[[i]][-idt]
}
if(length(zdata[[i]])<2) {
stop("length of data (w/o NA) must be more than 1")
}
# set data and time index
ser.times[[i]] <- as.numeric(time(zdata[[i]]))
# set difference of the data
ser.diffX[[i]] <- diff( as.numeric(zdata[[i]]) )
vol[i] <- sum(ser.diffX[[i]]^2)
}
theta <- matrix(0,d,d)
d.size <- d*(d-1)/2
crosscor <- vector(d.size,mode="list")
if(psd){
cormat <- diag(d)
if(missing(grid)){
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) == 1){
division <- rep(division,d.size)
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(time1),length(time2)))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- time2[1]-time1[1] # time lag (sec)
num1 <- time1[length(time1)]-time1[1] # elapsed time for series 1
num2 <- time2[length(time2)]-time2[1] # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
y <- seq(-num2-tmptheta,num1-tmptheta,length=n)[2:(n-1)]
tmp <- .C("HYcrosscorr",
as.integer(n-2),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(y/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
as.double(vol[i]),
as.double(vol[j]),
value=double(n-2),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -y[idx] # make the first timing of max or min
corr <- tmp[idx]
theta[i,j] <- mlag
cormat[i,j] <- corr
theta[j,i] <- -mlag
cormat[j,i] <- cormat[i,j]
crosscor[[num]] <- zoo(tmp,-y)
}
}
}else{
if(!is.list(grid)){
if(is.numeric(grid)){
grid <- data.frame(matrix(grid,length(grid),d.size))
}else{
print("llag:invalid grid")
return(NULL)
}
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
tmp <- .C("HYcrosscorr",
as.integer(length(grid[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(grid[[num]]/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
as.double(vol[i]),
as.double(vol[j]),
value=double(length(grid[[num]])),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -grid[[num]][idx] # make the first timing of max or min
cor <- tmp[idx]
theta[i,j] <- mlag
cormat[i,j] <- cor
theta[j,i] <- -mlag
cormat[j,i] <- cormat[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])
}
}
}
covmat <- diag(sqrt(vol))%*%cormat%*%diag(sqrt(vol))
}else{# non-psd
covmat <- diag(vol)
if(missing(grid)){
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) == 1){
division <- rep(division,d.size)
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(time1),length(time2)))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- time2[1]-time1[1] # time lag (sec)
num1 <- time1[length(time1)]-time1[1] # elapsed time for series 1
num2 <- time2[length(time2)]-time2[1] # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
y <- seq(-num2-tmptheta,num1-tmptheta,length=n)[2:(n-1)]
tmp <- .C("HYcrosscov",
as.integer(n-2),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(y/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
value=double(n-2),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -y[idx] # make the first timing of max or min
cov <- tmp[idx]
theta[i,j] <- mlag
covmat[i,j] <- cov
theta[j,i] <- -mlag
covmat[j,i] <- covmat[i,j]
crosscor[[num]] <- zoo(tmp,-y)/sqrt(vol[i]*vol[j])
}
}
}else{
if(!is.list(grid)){
if(is.numeric(grid)){
grid <- data.frame(matrix(grid,length(grid),d.size))
}else{
print("llag:invalid grid")
return(NULL)
}
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
tmp <- .C("HYcrosscov",
as.integer(length(grid[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(grid[[num]]/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
value=double(length(grid[[num]])),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -grid[[num]][idx] # make the first timing of max or min
cov <- tmp[idx]
theta[i,j] <- mlag
covmat[i,j] <- cov
theta[j,i] <- -mlag
covmat[j,i] <- covmat[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])/sqrt(vol[i]*vol[j])
}
}
}
cormat <- diag(1/sqrt(diag(covmat)))%*%covmat%*%diag(1/sqrt(diag(covmat)))
}
colnames(theta) <- names(zdata)
rownames(theta) <- names(zdata)
if(plot){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
plot(crosscor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=expression(theta),ylab=expression(U(theta)))
}
}
}
if(verbose==TRUE){
colnames(covmat) <- names(zdata)
rownames(covmat) <- names(zdata)
colnames(cormat) <- names(zdata)
rownames(cormat) <- names(zdata)
if(ccor){
return(list(lagcce=theta,covmat=covmat,cormat=cormat,ccor=crosscor))
}else{
return(list(lagcce=theta,covmat=covmat,cormat=cormat))
}
}else{
return(theta)
}
})
}
## Old version
if(0){
setMethod( "llag", "yuima.data", function(x,from=-Inf,to=Inf,division=FALSE,verbose=FALSE) {
if(!is(x)=="yuima.data"){
if(is(x)=="yuima"){
dat <- x@data
}else{
print("llag:invalid argument")
return(NULL)
}
}else{
dat <- x
}
d <- length(dat@zoo.data)
lagccep <- function(datp,theta){
time(datp[[2]]) <- time(datp[[2]])+theta
return(cce(setData(datp))$covmat[1,2])
}
lagcce <- function(datzoo,theta){
d <- dim(theta)[1]
lcmat <- cce(setData(datzoo))$covmat
for(i in 1:(d-1)){
for(j in (i+1):d){
datp <- datzoo[c(i,j)]
lcmat[i,j] <- lagccep(datp,theta[i,j])
lcmat[j,i] <- lcmat[i,j]
}
}
return(lcmat)
}
d.size <- d*(d-1)/2
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) != d.size){
division <- c(division,rep(FALSE,d.size - length(division)))
}
find_lag <- function(i,j){
datp <- dat@zoo.data[c(i,j)]
time1 <- time(datp[[1]])
time2 <- time(datp[[2]])
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(datp[[1]]),length(datp[[2]])))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- as.numeric(time2[1])-as.numeric(time1[1]) # time lag (sec)
num1 <- as.numeric(time1[length(time1)])-as.numeric(time1[1]) # elapsed time for series 1
num2 <- as.numeric(time2[length(time2)])-as.numeric(time2[1]) # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
y <- seq(-num2-tmptheta,num1-tmptheta,length=n)
tmp <- double(n)
for(i.tmp in 2:(n-1)){
tmp[i.tmp] <- lagccep(datp,y[i.tmp])
}
mat <- cbind(y[2:(n-1)],tmp[2:(n-1)])
#idx <- abs(mat[,2])==max(abs(mat[,2]))
#mlag <- mat[,1][idx][1] # make the first timing of max or min
#cov <- mat[,2][idx][1]
idx <- which.max(abs(mat[,2]))
mlag <- mat[,1][idx] # make the first timing of max or min
cov <- mat[,2][idx]
return(list(lag=-mlag,cov=cov))
}
theta <- matrix(numeric(d^2),ncol=d)
covmat <- cce(dat)$covmat
for(i in 1:(d-1)){
for(j in (i+1):d){
fl <- find_lag(i,j)
theta[i,j] <- fl$lag
covmat[i,j] <- fl$cov
theta[j,i] <- -theta[i,j]
covmat[j,i] <- covmat[i,j]
}
}
# covmat <- lagcce(dat@zoo.data,theta)
cormat <- diag(1/sqrt(diag(covmat)))%*%covmat%*%diag(1/sqrt(diag(covmat)))
if(verbose==TRUE){
return(list(lagcce=theta,covmat=covmat,cormat=cormat))
}else{
return(theta)
}
})
}
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Defines functions plot.yuima.llag print.yuima.llag llag.avar make.grid
#lead-lag estimation
#x:data
#setGeneric( "llag", function(x,verbose=FALSE) standardGeneric("llag") )
#setMethod( "llag", "yuima", function(x,verbose=FALSE) llag(x@data,verbose=verbose ))
#setMethod( "llag", "yuima.data", function(x,verbose=FALSE) {
#setGeneric( "llag",
# function(x,from=FALSE,to=FALSE,division=FALSE,verbose=FALSE)
# standardGeneric("llag") )
#setMethod( "llag", "yuima",
# function(x,from=FALSE,to=FALSE,division=FALSE,verbose=FALSE)
# llag(x@data,from=FALSE,to=FALSE,division=FALSE,verbose=verbose ))
#setMethod( "llag", "yuima.data", function(x,from=FALSE,to=FALSE,division=FALSE,verbose=FALSE) {
## function to make the grid if it is missing
make.grid <- function(d, d.size, x, from, to, division){
out <- vector(d.size, mode = "list")
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) == 1){
division <- rep(division,d.size)
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- as.numeric(time(x[[i]]))
time2 <- as.numeric(time(x[[j]]))
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(time1),length(time2)))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- time2[1]-time1[1] # time lag (sec)
num1 <- time1[length(time1)]-time1[1] # elapsed time for series 1
num2 <- time2[length(time2)]-time2[1] # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
out[[num]] <- seq(-num2-tmptheta,num1-tmptheta,length=n)[2:(n-1)]
}
}
return(out)
}
## function to compute asymptotic variances
llag.avar <- function(x, grid, bw, alpha, fisher, ser.diffX, ser.times, vol, cormat, ccor, idx, G, d, d.size, tol){
# treatment of the bandwidth
if(missing(bw)){
bw <- matrix(0, d, d)
for(i in 1:(d - 1)){
for(j in (i + 1):d){
Init <- min(ser.times[[i]][1], ser.times[[j]][1])
Term <- max(tail(ser.times[[i]], n = 1), tail(ser.times[[j]], n = 1))
bw[i, j] <- (Term - Init) * min(length(ser.times[[i]]), length(ser.times[[j]]))^(-0.45)
bw[j, i] <- bw[i, j]
}
}
}else{
bw <- bw/tol
}
bw <- matrix(bw, d, d)
p <- diag(d) # p-values
avar <- vector(d.size,mode="list") # asymptotic variances
CI <- vector(d.size,mode="list") # confidence intervals
names(avar) <- names(ccor)
names(CI) <- names(ccor)
vv <- (2/3) * sapply(ser.diffX, FUN = function(x) sum(x^4)) # AVAR for RV
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
## computing conficence intervals
N.max <- max(length(time1), length(time2))
tmp <- rev(as.numeric(ccor[[num]]))
d1 <- -0.5 * tmp * sqrt(vol[j]/vol[i])
d2 <- -0.5 * tmp * sqrt(vol[i]/vol[j])
avar.tmp <- .C("hycrossavar",
as.double(G[[num]]),
as.double(time1),
as.double(time2),
as.integer(length(G[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(x[[i]]),
as.double(x[[j]]),
as.integer(N.max),
as.double(bw[i, j]),
as.double(vv[i]),
as.double(vv[j]),
as.double(d1^2),
as.double(d2^2),
as.double(2 * d1),
as.double(2 * d2),
as.double(2 * d1 * d2),
covar = double(length(G[[num]])),
corr = double(length(G[[num]])),
PACKAGE = "yuima")$corr / (vol[i] * vol[j])
#avar[[num]][avar[[num]] <= 0] <- NA
if(fisher == TRUE){
z <- atanh(tmp) # the Fisher z transformation of the estimated correlation
se.z <- sqrt(avar.tmp)/(1 - tmp^2)
p[i,j] <- pchisq((atanh(cormat[i,j])/se.z[idx[num]])^2, df=1, lower.tail=FALSE)
CI[[num]] <- zoo(tanh(qnorm(1 - alpha/2) * se.z), -grid[[num]])
}else{
p[i,j] <- pchisq(cormat[i,j]^2/avar.tmp[idx[num]], df=1, lower.tail=FALSE)
c.alpha <- sqrt(qchisq(alpha, df=1, lower.tail = FALSE) * avar.tmp)
CI[[num]] <- zoo(c.alpha, -grid[[num]])
}
p[j,i] <- p[i,j]
avar[[num]] <- zoo(avar.tmp, -grid[[num]])
}
}
return(list(p = p, avar = avar, CI = CI))
}
## main body
setGeneric( "llag", function(x, from = -Inf, to = Inf, division = FALSE,
verbose = (ci || ccor), grid, psd = TRUE, plot = ci,
ccor = ci, ci = FALSE, alpha = 0.01, fisher = TRUE, bw, tol = 1e-6) standardGeneric("llag") )
## yuima-method
setMethod("llag", "yuima", function(x, from, to, division, verbose, grid, psd, plot,
ccor, ci, alpha, fisher, bw, tol)
llag(x@data, from, to, division, verbose, grid, psd, plot, ccor, ci, alpha, fisher, bw, tol))
## yuima.data-method
setMethod("llag", "yuima.data", function(x, from, to, division, verbose, grid, psd, plot,
ccor, ci, alpha, fisher, bw, tol)
llag(x@zoo.data, from, to, division, verbose, grid, psd, plot, ccor, ci, alpha, fisher, bw, tol))
## list-method
setMethod("llag", "list", function(x, from, to, division, verbose, grid, psd, plot,
ccor, ci, alpha, fisher, bw, tol) {
d <- length(x)
d.size <- d*(d-1)/2
# allocate memory
ser.times <- vector(d, mode="list") # time index in 'x'
ser.diffX <- vector(d, mode="list") # difference of data
vol <- double(d)
# treatment of the grid (2016-07-04: we implement this before the NA treatment)
if(missing(grid))
grid <- make.grid(d, d.size, x, from, to, division)
# Set the tolerance to avoid numerical erros in comparison
#tol <- 1e-6
for(i in 1:d){
# NA data must be skipped
idt <- which(is.na(x[[i]]))
if(length(idt>0)){
x[[i]] <- x[[i]][-idt]
}
if(length(x[[i]])<2) {
stop("length of data (w/o NA) must be more than 1")
}
# set data and time index
ser.times[[i]] <- as.numeric(time(x[[i]]))/tol
# set difference of the data
ser.diffX[[i]] <- diff( as.numeric(x[[i]]) )
vol[i] <- sum(ser.diffX[[i]]^2)
}
theta <- matrix(0,d,d)
#d.size <- d*(d-1)/2
crosscor <- vector(d.size,mode="list")
idx <- integer(d.size)
# treatment of the grid
#if(missing(grid))
# grid <- make.grid(d, d.size, x, from, to, division)
if(is.list(grid)){
G <- relist(unlist(grid)/tol, grid)
}else{
if(is.numeric(grid)){
G <- data.frame(matrix(grid/tol,length(grid),d.size))
grid <- data.frame(matrix(grid,length(grid),d.size))
}else{
print("llag:invalid grid")
return(NULL)
}
}
# core part
if(psd){ # positive semidefinite correction is implemented
cormat <- diag(d)
LLR <- diag(d)
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
names(crosscor)[num] <- paste("(",i,",",j,")", sep = "")
tmp <- .C("HYcrosscorr2",
as.integer(length(G[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(G[[num]]),
as.double(time1),
as.double(time2),
#double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
as.double(vol[i]),
as.double(vol[j]),
value=double(length(G[[num]])),
PACKAGE = "yuima")$value
idx[num] <- which.max(abs(tmp))
mlag <- -grid[[num]][idx[num]] # make the first timing of max or min
cor <- tmp[idx[num]]
theta[i,j] <- mlag
cormat[i,j] <- cor
theta[j,i] <- -mlag
cormat[j,i] <- cormat[i,j]
LLR[i,j] <- sum(tmp[grid[[num]] < 0]^2)/sum(tmp[grid[[num]] > 0]^2)
LLR[j,i] <- 1/LLR[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])
}
}
covmat <- diag(sqrt(vol))%*%cormat%*%diag(sqrt(vol))
}else{# non-psd
covmat <- diag(vol)
LLR <- diag(d)
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
names(crosscor)[num] <- paste("(",i,",",j,")", sep = "")
tmp <- .C("HYcrosscov2",
as.integer(length(G[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(G[[num]]),
as.double(time1),
as.double(time2),
#double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
value=double(length(G[[num]])),
PACKAGE = "yuima")$value
idx[num] <- which.max(abs(tmp))
mlag <- -grid[[num]][idx[num]] # make the first timing of max or min
cov <- tmp[idx[num]]
theta[i,j] <- mlag
covmat[i,j] <- cov
theta[j,i] <- -mlag
covmat[j,i] <- covmat[i,j]
LLR[i,j] <- sum(tmp[grid[[num]] < 0]^2)/sum(tmp[grid[[num]] > 0]^2)
LLR[j,i] <- 1/LLR[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])/sqrt(vol[i]*vol[j])
}
}
cormat <- diag(1/sqrt(diag(covmat)))%*%covmat%*%diag(1/sqrt(diag(covmat)))
}
if(ci){ # computing confidence intervals
out <- llag.avar(x = x, grid = grid, bw = bw, alpha = alpha, fisher = fisher,
ser.diffX = ser.diffX, ser.times = ser.times,
vol = vol, cormat = cormat, ccor = crosscor, idx = idx,
G = G, d = d, d.size = d.size, tol = tol)
p <- out$p
CI <- out$CI
avar <- out$avar
colnames(theta) <- names(x)
rownames(theta) <- names(x)
colnames(p) <- names(x)
rownames(p) <- names(x)
if(plot){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
y.max <- max(abs(as.numeric(crosscor[[num]])),as.numeric(CI[[num]]))
plot(crosscor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=expression(theta),ylab=expression(U(theta)),
ylim=c(-y.max,y.max))
lines(CI[[num]],lty=2,col="blue")
lines(-CI[[num]],lty=2,col="blue")
}
}
}
if(verbose==TRUE){
colnames(covmat) <- names(x)
rownames(covmat) <- names(x)
colnames(cormat) <- names(x)
rownames(cormat) <- names(x)
colnames(LLR) <- names(x)
rownames(LLR) <- names(x)
if(ccor){
result <- list(lagcce=theta,p.values=p,covmat=covmat,cormat=cormat,LLR=LLR,ccor=crosscor,avar=avar)
}else{
result <- list(lagcce=theta,p.values=p,covmat=covmat,cormat=cormat,LLR=LLR)
}
}else{
return(theta)
}
}else{
colnames(theta) <- names(x)
rownames(theta) <- names(x)
if(plot){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
plot(crosscor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=expression(theta),ylab=expression(U(theta)))
}
}
}
if(verbose==TRUE){
colnames(covmat) <- names(x)
rownames(covmat) <- names(x)
colnames(cormat) <- names(x)
rownames(cormat) <- names(x)
colnames(LLR) <- names(x)
rownames(LLR) <- names(x)
if(ccor){
result <- list(lagcce=theta,covmat=covmat,cormat=cormat,LLR=LLR,ccor=crosscor)
}else{
result <- list(lagcce=theta,covmat=covmat,cormat=cormat,LLR=LLR)
}
}else{
return(theta)
}
}
class(result) <- "yuima.llag"
return(result)
})
# print method for yuima.llag-class
print.yuima.llag <- function(x, ...){
if(is.null(x$p.values)){
cat("Estimated lead-lag parameters\n")
print(x$lagcce, ...)
cat("Corresponding covariance matrix\n")
print(x$covmat, ...)
cat("Corresponding correlation matrix\n")
print(x$cormat, ...)
cat("Lead-lag ratio\n")
print(x$LLR, ...)
}else{
cat("Estimated lead-lag parameters\n")
print(x$lagcce, ...)
cat("Corresponding p-values\n")
print(x$p.values, ...)
cat("Corresponding covariance matrix\n")
print(x$covmat, ...)
cat("Corresponding correlation matrix\n")
print(x$cormat, ...)
cat("Lead-lag ratio\n")
print(x$LLR, ...)
}
}
# plot method for yuima.llag-class
plot.yuima.llag <- function(x, alpha = 0.01, fisher = TRUE,
main = NULL, xlab = NULL, ylab = NULL, ...){
if(is.null(x$ccor)){
warning("cross-correlation functions were not returned by llag. Set verbose = TRUE and ccor = TRUE to return them.",
call. = FALSE)
return(NULL)
}else{
if(is.null(xlab)) xlab <- expression(theta)
if(is.null(ylab)) ylab <- expression(U(theta))
d <- nrow(x$LLR)
if(is.null(x$avar)){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(is.null(main)){
plot(x$ccor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=xlab,ylab=ylab)
}else{
plot(x$ccor[[num]],main=main,xlab=xlab,ylab=ylab)
}
}
}
}else{
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
G <- time(x$ccor[[num]])
if(fisher == TRUE){
z <- atanh(x$ccor[[num]]) # the Fisher z transformation of the estimated correlation
se.z <- sqrt(x$avar[[num]])/(1 - x$ccor[[num]]^2)
CI <- zoo(tanh(qnorm(1 - alpha/2) * se.z), G)
}else{
c.alpha <- sqrt(qchisq(alpha, df=1, lower.tail = FALSE) * x$avar[[num]])
CI <- zoo(c.alpha, G)
}
y.max <- max(abs(as.numeric(x$ccor[[num]])),as.numeric(CI))
if(is.null(main)){
plot(x$ccor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=xlab,ylab=ylab,ylim=c(-y.max,y.max))
}else{
plot(x$ccor[[num]],main = main,xlab=xlab,ylab=ylab,
ylim=c(-y.max,y.max))
}
lines(CI,lty=2,col="blue")
lines(-CI,lty=2,col="blue")
}
}
}
}
}
## Old version until Oct. 10, 2015
if(0){
setGeneric( "llag",
function(x,from=-Inf,to=Inf,division=FALSE,verbose=FALSE,grid,psd=TRUE,
plot=FALSE,ccor=FALSE)
standardGeneric("llag") )
setMethod( "llag", "yuima",
function(x,from=-Inf,to=Inf,division=FALSE,verbose=FALSE,grid,psd=TRUE,
plot=FALSE,ccor=FALSE)
llag(x@data,from=from,to=to,division=division,verbose=verbose,grid=grid,
psd=psd,plot=plot))
setMethod( "llag", "yuima.data", function(x,from=-Inf,to=Inf,division=FALSE,
verbose=FALSE,grid,psd=TRUE,
plot=FALSE,ccor=FALSE) {
if((is(x)=="yuima")||(is(x)=="yuima.data")){
zdata <- get.zoo.data(x)
}else{
print("llag:invalid argument")
return(NULL)
}
d <- length(zdata)
# allocate memory
ser.times <- vector(d, mode="list") # time index in 'x'
ser.diffX <- vector(d, mode="list") # difference of data
vol <- double(d)
# Set the tolerance to avoid numerical erros in comparison
tol <- 1e-6
for(i in 1:d){
# NA data must be skipped
idt <- which(is.na(zdata[[i]]))
if(length(idt>0)){
zdata[[i]] <- zdata[[i]][-idt]
}
if(length(zdata[[i]])<2) {
stop("length of data (w/o NA) must be more than 1")
}
# set data and time index
ser.times[[i]] <- as.numeric(time(zdata[[i]]))
# set difference of the data
ser.diffX[[i]] <- diff( as.numeric(zdata[[i]]) )
vol[i] <- sum(ser.diffX[[i]]^2)
}
theta <- matrix(0,d,d)
d.size <- d*(d-1)/2
crosscor <- vector(d.size,mode="list")
if(psd){
cormat <- diag(d)
if(missing(grid)){
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) == 1){
division <- rep(division,d.size)
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(time1),length(time2)))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- time2[1]-time1[1] # time lag (sec)
num1 <- time1[length(time1)]-time1[1] # elapsed time for series 1
num2 <- time2[length(time2)]-time2[1] # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
y <- seq(-num2-tmptheta,num1-tmptheta,length=n)[2:(n-1)]
tmp <- .C("HYcrosscorr",
as.integer(n-2),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(y/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
as.double(vol[i]),
as.double(vol[j]),
value=double(n-2),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -y[idx] # make the first timing of max or min
corr <- tmp[idx]
theta[i,j] <- mlag
cormat[i,j] <- corr
theta[j,i] <- -mlag
cormat[j,i] <- cormat[i,j]
crosscor[[num]] <- zoo(tmp,-y)
}
}
}else{
if(!is.list(grid)){
if(is.numeric(grid)){
grid <- data.frame(matrix(grid,length(grid),d.size))
}else{
print("llag:invalid grid")
return(NULL)
}
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
tmp <- .C("HYcrosscorr",
as.integer(length(grid[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(grid[[num]]/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
as.double(vol[i]),
as.double(vol[j]),
value=double(length(grid[[num]])),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -grid[[num]][idx] # make the first timing of max or min
cor <- tmp[idx]
theta[i,j] <- mlag
cormat[i,j] <- cor
theta[j,i] <- -mlag
cormat[j,i] <- cormat[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])
}
}
}
covmat <- diag(sqrt(vol))%*%cormat%*%diag(sqrt(vol))
}else{# non-psd
covmat <- diag(vol)
if(missing(grid)){
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) == 1){
division <- rep(division,d.size)
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(time1),length(time2)))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- time2[1]-time1[1] # time lag (sec)
num1 <- time1[length(time1)]-time1[1] # elapsed time for series 1
num2 <- time2[length(time2)]-time2[1] # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
y <- seq(-num2-tmptheta,num1-tmptheta,length=n)[2:(n-1)]
tmp <- .C("HYcrosscov",
as.integer(n-2),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(y/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
value=double(n-2),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -y[idx] # make the first timing of max or min
cov <- tmp[idx]
theta[i,j] <- mlag
covmat[i,j] <- cov
theta[j,i] <- -mlag
covmat[j,i] <- covmat[i,j]
crosscor[[num]] <- zoo(tmp,-y)/sqrt(vol[i]*vol[j])
}
}
}else{
if(!is.list(grid)){
if(is.numeric(grid)){
grid <- data.frame(matrix(grid,length(grid),d.size))
}else{
print("llag:invalid grid")
return(NULL)
}
}
for(i in 1:(d-1)){
for(j in (i+1):d){
time1 <- ser.times[[i]]
time2 <- ser.times[[j]]
num <- d*(i-1) - (i-1)*i/2 + (j-i)
tmp <- .C("HYcrosscov",
as.integer(length(grid[[num]])),
as.integer(length(time1)),
as.integer(length(time2)),
as.double(grid[[num]]/tol),
as.double(time1/tol),
as.double(time2/tol),
double(length(time2)),
as.double(ser.diffX[[i]]),
as.double(ser.diffX[[j]]),
value=double(length(grid[[num]])),
PACKAGE = "yuima")$value
idx <- which.max(abs(tmp))
mlag <- -grid[[num]][idx] # make the first timing of max or min
cov <- tmp[idx]
theta[i,j] <- mlag
covmat[i,j] <- cov
theta[j,i] <- -mlag
covmat[j,i] <- covmat[i,j]
crosscor[[num]] <- zoo(tmp,-grid[[num]])/sqrt(vol[i]*vol[j])
}
}
}
cormat <- diag(1/sqrt(diag(covmat)))%*%covmat%*%diag(1/sqrt(diag(covmat)))
}
colnames(theta) <- names(zdata)
rownames(theta) <- names(zdata)
if(plot){
for(i in 1:(d-1)){
for(j in (i+1):d){
num <- d*(i-1) - (i-1)*i/2 + (j-i)
plot(crosscor[[num]],
main=paste(i,"vs",j,"(positive",expression(theta),"means",i,"leads",j,")"),
xlab=expression(theta),ylab=expression(U(theta)))
}
}
}
if(verbose==TRUE){
colnames(covmat) <- names(zdata)
rownames(covmat) <- names(zdata)
colnames(cormat) <- names(zdata)
rownames(cormat) <- names(zdata)
if(ccor){
return(list(lagcce=theta,covmat=covmat,cormat=cormat,ccor=crosscor))
}else{
return(list(lagcce=theta,covmat=covmat,cormat=cormat))
}
}else{
return(theta)
}
})
}
## Old version
if(0){
setMethod( "llag", "yuima.data", function(x,from=-Inf,to=Inf,division=FALSE,verbose=FALSE) {
if(!is(x)=="yuima.data"){
if(is(x)=="yuima"){
dat <- x@data
}else{
print("llag:invalid argument")
return(NULL)
}
}else{
dat <- x
}
d <- length(dat@zoo.data)
lagccep <- function(datp,theta){
time(datp[[2]]) <- time(datp[[2]])+theta
return(cce(setData(datp))$covmat[1,2])
}
lagcce <- function(datzoo,theta){
d <- dim(theta)[1]
lcmat <- cce(setData(datzoo))$covmat
for(i in 1:(d-1)){
for(j in (i+1):d){
datp <- datzoo[c(i,j)]
lcmat[i,j] <- lagccep(datp,theta[i,j])
lcmat[j,i] <- lcmat[i,j]
}
}
return(lcmat)
}
d.size <- d*(d-1)/2
if(length(from) != d.size){
from <- c(from,rep(-Inf,d.size - length(from)))
}
if(length(to) != d.size){
to <- c(to,rep(Inf,d.size - length(to)))
}
if(length(division) != d.size){
division <- c(division,rep(FALSE,d.size - length(division)))
}
find_lag <- function(i,j){
datp <- dat@zoo.data[c(i,j)]
time1 <- time(datp[[1]])
time2 <- time(datp[[2]])
# calculate the maximum of correlation by substituting theta to lagcce
#n:=2*length(data)
num <- d*(i-1) - (i-1)*i/2 + (j-i)
if(division[num]==FALSE){
n <- round(2*max(length(datp[[1]]),length(datp[[2]])))+1
}else{
n <- division[num]
}
# maximum value of lagcce
tmptheta <- as.numeric(time2[1])-as.numeric(time1[1]) # time lag (sec)
num1 <- as.numeric(time1[length(time1)])-as.numeric(time1[1]) # elapsed time for series 1
num2 <- as.numeric(time2[length(time2)])-as.numeric(time2[1]) # elapsed time for series 2
# modified
if(is.numeric(from[num])==TRUE && is.numeric(to[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(from[num])==TRUE){
num2 <- min(-from[num],num2+tmptheta)
num1 <- num1-tmptheta
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}else if(is.numeric(to[num])==TRUE){
num2 <- num2+tmptheta
num1 <- min(to[num],num1-tmptheta)
tmptheta <- 0
if(-num2 >= num1){
print("llag:invalid range")
return(NULL)
}
}
y <- seq(-num2-tmptheta,num1-tmptheta,length=n)
tmp <- double(n)
for(i.tmp in 2:(n-1)){
tmp[i.tmp] <- lagccep(datp,y[i.tmp])
}
mat <- cbind(y[2:(n-1)],tmp[2:(n-1)])
#idx <- abs(mat[,2])==max(abs(mat[,2]))
#mlag <- mat[,1][idx][1] # make the first timing of max or min
#cov <- mat[,2][idx][1]
idx <- which.max(abs(mat[,2]))
mlag <- mat[,1][idx] # make the first timing of max or min
cov <- mat[,2][idx]
return(list(lag=-mlag,cov=cov))
}
theta <- matrix(numeric(d^2),ncol=d)
covmat <- cce(dat)$covmat
for(i in 1:(d-1)){
for(j in (i+1):d){
fl <- find_lag(i,j)
theta[i,j] <- fl$lag
covmat[i,j] <- fl$cov
theta[j,i] <- -theta[i,j]
covmat[j,i] <- covmat[i,j]
}
}
# covmat <- lagcce(dat@zoo.data,theta)
cormat <- diag(1/sqrt(diag(covmat)))%*%covmat%*%diag(1/sqrt(diag(covmat)))
if(verbose==TRUE){
return(list(lagcce=theta,covmat=covmat,cormat=cormat))
}else{
return(theta)
}
})
}
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