Mstep | R Documentation |
Update \sigma_\eta,\sigma_\epsilon
based on estimate of A and
conditional expecation and covariance from expectation step.
Mstep(Y,A,EXtT,EXtt,EXtt1,is_MLE=FALSE)
Y |
observations of time series, a p by T matrix. |
A |
current estimate of transition matrix |
EXtT |
a p by T matrix of column |
EXtt |
a p by p by T tensor of first-two-mode slice |
EXtt1 |
a p by p by T-1 matrix of first-two-mode slice |
is_MLE |
logic; if true, use naive MLE of transition matrix, by conditional expecation and covariance from expecation step, to update error variances. Otherwise, use input argument |
a list of estimates of error standard deviations.
sig_eta | estimate of \sigma_\eta . |
sig_epsilon | estimate of \sigma_\epsilon . |
A | naive MLE of transition matrix A by conditional expecation and covariance from expecation step. Exist if is_MLE=TRUE . |
Xiang Lyu, Jian Kang, Lexin Li
p= 2; Ti=10 # dimension and time
A=diag(1,p) # transition matrix
sig_eta=sig_epsilon=0.2 # error std
Y=array(0,dim=c(p,Ti)) #observation t=1, ...., Ti
X=array(0,dim=c(p,Ti)) #latent t=1, ...., T
Ti_burnin=100 # time for burn-in to stationarity
for (t in 1:(Ti+Ti_burnin)) {
if (t==1){
x1=rnorm(p)
} else if (t<=Ti_burnin) { # burn in
x1=A%*%x1+rnorm(p,mean=0,sd=sig_eta)
} else if (t==(Ti_burnin+1)){ # time series used for learning
X[,t-Ti_burnin]=x1
Y[,t-Ti_burnin]=X[,t-Ti_burnin]+rnorm(p,mean=0,sd=sig_epsilon)
} else {
X[,t- Ti_burnin]=A%*%X[,t-1- Ti_burnin]+rnorm(p,mean=0,sd=sig_eta)
Y[,t- Ti_burnin]=X[,t- Ti_burnin]+rnorm(p,mean=0,sd=sig_epsilon)
}
}
# expectation step
Efit=Estep(Y,A,sig_eta,sig_epsilon,x1,diag(1,p))
EXtT=Efit[["EXtT"]]
EXtt=Efit[["EXtt"]]
EXtt1=Efit[["EXtt1"]]
# maximization step for error standard deviations
Mfit=Mstep(Y,A,EXtT,EXtt,EXtt1)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.