R/VARMACpp.R In MTS: All-Purpose Toolkit for Analyzing Multivariate Time Series (MTS) and Estimating Multivariate Volatility Models

```"VARMACpp" <- function(da,p=0,q=0,include.mean=T,fixed=NULL,beta=NULL,sebeta=NULL,prelim=F,details=F,thres=2.0){
# Estimation of a vector ARMA model using conditional MLE (Gaussian dist)
#
# When prelim=TRUE, fixed is assigned based on the results of AR approximation.
# Here "thres" is used only when prelim = TRUE.
#
if(!is.matrix(da))da=as.matrix(da)
nT=dim(da)[1];   k=dim(da)[2]
# basic setup.
if(p < 0)p=0
if(q < 0)q=0
if((p+q) < 1)p=1
pqmax=max(p,q)
kq=k*q
kp=k*p
#
iniEST <- function(y,x,p,q,include.mean){
# use residuals of a long VAR model to obtain initial estimates of
# VARMA coefficients.
if(!is.matrix(y))y=as.matrix(y)
if(!is.matrix(x))x=as.matrix(x)
nT=dim(y)[1]
k=dim(y)[2]
pq=max(p,q)
ist=1+pq
ne=nT-pq
if(include.mean){
xmtx=matrix(1,ne,1)
}
else {
xmtx=NULL
}
ymtx=as.matrix(y[ist:nT,])
if(p > 0){
for (j in 1:p){
xmtx=cbind(xmtx,y[(ist-j):(nT-j),])
}
}
if(q > 0){
for (j in 1:q){
xmtx=cbind(xmtx,x[(ist-j):(nT-j),])
}
}
xmtx=as.matrix(xmtx)
xtx=crossprod(xmtx,xmtx)
xty=crossprod(xmtx,ymtx)
xtxinv=solve(xtx)
beta=xtxinv%*%xty
resi= ymtx - xmtx%*%beta
sse=crossprod(resi,resi)/ne
dd=diag(xtxinv)
sebeta=NULL
for (j in 1:k){
se=sqrt(dd*sse[j,j])
sebeta=cbind(sebeta,se)
}
iniEST <- list(estimates=beta,se=sebeta)
}

if(length(fixed) < 1){
m1=VARorder(da,p+q+9,output=FALSE)
porder=m1\$aicor
if(porder < 1)porder=1
m2=VAR(da,porder,output=FALSE)
y=da[(porder+1):nT,]
x=m2\$residuals
m3=iniEST(y,x,p,q,include.mean)
beta=m3\$estimates
sebeta=m3\$se
nr=dim(beta)[1]
### Preliminary simplification
if(prelim){
fixed = matrix(0,nr,k)
for (j in 1:k){
tt=beta[,j]/sebeta[,j]
idx=c(1:nr)[abs(tt) >= thres]
fixed[idx,j]=1
}
}
if(length(fixed)==0){fixed=matrix(1,nr,k)}
}
# Identify parameters to be estimated.
par=NULL
separ=NULL
ist=0
if(include.mean){
jdx=c(1:k)[fixed[1,]==1]
if(length(jdx) > 0){
par=beta[1,jdx]
separ=sebeta[1,jdx]
}
ist=1
}
if(p > 0){
for (j in 1:k){
idx=c(1:kp)[fixed[(ist+1):(ist+kp),j]==1]
if(length(idx) > 0){
tmp=beta[(ist+1):(ist+kp),j]
setmp=sebeta[(ist+1):(ist+kp),j]
par=c(par,tmp[idx])
separ=c(separ,setmp[idx])
}
#end of j-loop
}
ist=ist+kp
}
#
if(q > 0){
for (j in 1:k){
idx=c(1:kq)[fixed[(ist+1):(ist+kq),j]==1]
if(length(idx) > 0){
tmp=beta[(ist+1):(ist+kq),j]
setmp=sebeta[(ist+1):(ist+kq),j]
par=c(par,tmp[idx])
separ=c(separ,setmp[idx])
}
}
}
#########
cat("Number of parameters: ",length(par),"\n")
cat("initial estimates: ",round(par,4),"\n")
### Set up lower and upper bounds
lowerBounds=par; upperBounds=par
for (j in 1:length(par)){
lowerBounds[j] = par[j]-2*separ[j]
upperBounds[j] = par[j]+2*separ[j]
}
cat("Par. lower-bounds: ",round(lowerBounds,4),"\n")
cat("Par. upper-bounds: ",round(upperBounds,4),"\n")
#### likelihood function
LLKVARMACpp <- function(par,zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed) {
k    = dim(zt)[2]
nT    = dim(zt)[1]
pqmax = max(p, q)

ListResiduals = .Call("GetVarmaResiduals", zt, fixed, par, p, q, include.mean)
at  = do.call(rbind, as.list(ListResiduals))
sig = t(at) %*% at/(nT-pqmax)
ll  = dmvnorm(at,rep(0,k),sig)
LLKVARMACpp =-sum(log(ll))
LLKVARMACpp
}

# Step 5: Estimate Parameters and Compute Numerically Hessian:
if(details){
fit = nlminb(start = par, objective = LLKVARMACpp,zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed,
lower = lowerBounds, upper = upperBounds, control = list(trace=3))
}
else {
fit = nlminb(start = par, objective = LLKVARMACpp, zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed,
lower = lowerBounds, upper = upperBounds)
}
epsilon = 0.0001 * fit\$par
npar=length(par)
Hessian = matrix(0, ncol = npar, nrow = npar)
for (i in 1:npar) {
for (j in 1:npar) {
x1 = x2 = x3 = x4  = fit\$par
x1[i] = x1[i] + epsilon[i]; x1[j] = x1[j] + epsilon[j]
x2[i] = x2[i] + epsilon[i]; x2[j] = x2[j] - epsilon[j]
x3[i] = x3[i] - epsilon[i]; x3[j] = x3[j] + epsilon[j]
x4[i] = x4[i] - epsilon[i]; x4[j] = x4[j] - epsilon[j]
Hessian[i, j] = (LLKVARMACpp(x1,zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed)
-LLKVARMACpp(x2,zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed)
-LLKVARMACpp(x3,zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed)
+LLKVARMACpp(x4,zt=da,p=p,q=q,include.mean=include.mean,fixed=fixed))/
(4*epsilon[i]*epsilon[j])
}
}
est=fit\$par
cat("Final   Estimates: ",est,"\n")
# Step 6: Create and Print Summary Report:
se.coef = sqrt(diag(solve(Hessian)))
tval = fit\$par/se.coef
matcoef = cbind(fit\$par, se.coef, tval, 2*(1-pnorm(abs(tval))))
dimnames(matcoef) = list(names(tval), c(" Estimate",
" Std. Error", " t value", "Pr(>|t|)"))
cat("\nCoefficient(s):\n")
printCoefmat(matcoef, digits = 4, signif.stars = TRUE)
#
### restore estimates to the format of unconstrained case for printing purpose.
#### icnt: parameter count
#### ist: location count
ist=0
icnt = 0
Ph0=rep(0,k)
sePh0=rep(0,k)
beta=NULL
sebeta=NULL
if(include.mean){
idx=c(1:k)[fixed[1,]==1]
icnt=length(idx)
if(icnt > 0){
Ph0[idx]=est[1:icnt]
sePh0[idx]=se.coef[1:icnt]
}
ist=1
beta=rbind(beta,Ph0)
sebeta=rbind(sebeta,sePh0)
}
PH=NULL
sePH=NULL
if(p > 0){
PH=matrix(0,kp,k)
sePH=matrix(0,kp,k)
for (j in 1:k){
idx=c(1:kp)[fixed[(ist+1):(ist+kp),j]==1]
jdx=length(idx)
if(jdx > 0){
PH[idx,j]=est[(icnt+1):(icnt+jdx)]
sePH[idx,j]=se.coef[(icnt+1):(icnt+jdx)]
icnt=icnt+jdx
}
# end of j-loop
}
#end of if (p > 0)
ist=ist+kp
beta=rbind(beta,PH)
sebeta=rbind(sebeta,sePH)
}
#
TH=NULL
seTH=NULL
if(q > 0){
TH=matrix(0,kq,k)
seTH=matrix(0,kq,k)
for (j in 1:k){
idx=c(1:kq)[fixed[(ist+1):(ist+kq),j]==1]
jdx=length(idx)
if(jdx > 0){
TH[idx,j]=est[(icnt+1):(icnt+jdx)]
seTH[idx,j]=se.coef[(icnt+1):(icnt+jdx)]
icnt=icnt+jdx
}
# end of j-loop
}
# end of if(q > 0).
beta=rbind(beta,TH)
sebeta=rbind(sebeta,seTH)
}
#########
cat("---","\n")
cat("Estimates in matrix form:","\n")
if(include.mean){
cat("Constant term: ","\n")
cat("Estimates: ",Ph0,"\n")
}
if(p > 0){
cat("AR coefficient matrix","\n")
jcnt=0
for (i in 1:p){
cat("AR(",i,")-matrix","\n")
ph=t(PH[(jcnt+1):(jcnt+k),])
print(ph,digits=3)
jcnt=jcnt+k
}
# end of if (p > 0)
}
if(q > 0){
cat("MA coefficient matrix","\n")
icnt=0
for (i in 1:q){
cat("MA(",i,")-matrix","\n")
theta=-t(TH[(icnt+1):(icnt+k),])
print(theta,digits=3)
icnt=icnt+k
}
# end of the statement if(q > 0)
}
##### Compute the residuals
zt=da
ist=pqmax+1
#### consider the case t from 1 to pqmatx
at=matrix((zt[1,]-Ph0),1,k)
if(pqmax > 1){
for (t in 2:pqmax){
tmp=matrix((zt[t,]-Ph0),1,k)
if(p > 0){
for (j in 1:p){
if((t-j) > 0){
jdx=(j-1)*k
tmp1=matrix(zt[(t-j),],1,k)%*%as.matrix(PH[(jdx+1):(jdx+k),])
tmp=tmp-tmp1
}
# end of j-loop
}
# end of if(p > 0) statement
}
#
if(q > 0){
for (j in 1:q){
jdx=(j-1)*k
if((t-j)>0){
tmp2=matrix(at[(t-j),],1,k)%*%as.matrix(TH[(jdx+1):(jdx+k),])
tmp=tmp-tmp2
}
#end of j-loop
}
#end of if(q > 0) statement
}
at=rbind(at,tmp)
# end of for(t in 2:pqmax)
}
# end of if(pqmax > 1) statement
}

### for t from ist on
Pcnt = NULL
idim=kp+kq
if(include.mean){
Pcnt=c(1)
idim=idim+1
}
#
for (t in ist:nT){
Past=NULL
if(p > 0){
for (j in 1:p){
Past=c(Past,zt[(t-j),])
}
}
if(q > 0){
for (j in 1:q){
Past=c(Past,at[(t-j),])
}
}
tmp = matrix(c(Pcnt,Past),1,idim)%*%beta
tmp3=zt[t,]-tmp
at=rbind(at,tmp3)
}
#### skip the first max(p,q) residuals.
at=at[(ist:nT),]
sig=t(at)%*%at/(nT-pqmax)
##
cat(" ","\n")
cat("Residuals cov-matrix:","\n")
print(sig)
dd=det(sig)
d1=log(dd)
aic=d1+2*npar/nT
bic=d1+log(nT)*npar/nT
cat("----","\n")
cat("aic= ",aic,"\n")
cat("bic= ",bic,"\n")
if(length(PH) > 0)PH=t(PH)
if(length(TH) > 0)TH=-t(TH)

VARMACpp <- list(data=da,ARorder=p,MAorder=q,cnst=include.mean,coef=beta,secoef=sebeta,residuals=at,Sigma=sig,aic=aic,bic=bic,Phi=PH,Theta=TH,Ph0=Ph0)
}
```

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MTS documentation built on May 29, 2017, 5:15 p.m.