R/Mstep.hh.ridge.MSAR.R

In NHMSAR: Non-Homogeneous Markov Switching Autoregressive Models

Mstep.hh.ridge.MSAR <-
function(data,theta,FB,lambda=lambda)  {  
	T=dim(data)[1]
	N.samples = dim(as.array(data))[2] 
	d = dim(as.array(data))[3]
	if(is.null(d)|is.na(d)) {d = 1}
    M <- attributes(theta)$NbRegimes
    p <- attributes(theta)$order
	order <- max(p,1)
	data = array(data,c(T,N.samples,d))
	data2 = array(0,c(order*d,T-order+1,N.samples))
	cpt=1
    for (o in order:1) {
    	for (kd in 1:d) {
    		 data2[cpt,,] = data[o:(T-order+o),,kd]
    		 cpt =cpt+1
    	}
    }
        #browser()
    T = length(o:(dim(data)[1]-order+o))
	exp_num_trans = 0
	exp_num_visit = 0
	exp_num_visits1 = 0
	postmix = 0
	m = matrix(0,d*order,M) ; m_1 = m ; c = matrix(0,M,1) ; s=c ; 
    op = array(0,c(d*order,d*order,M) ); op_1 = op ; op_2 = op_1 ;

	for (ex in 1:N.samples) {
		obs = array(data2[,,ex],c(d*order,T))
		xit  = array(FB$probSS[,,,ex],c(M,M,T-2))
		gamma = matrix(FB$probS[ex,1:(T-1),],T-1,M)
		exp_num_trans = exp_num_trans+apply(xit,c(1,2),sum)
		exp_num_visits1 = exp_num_visits1+gamma[1,]
		postmix = postmix+apply(gamma,2,sum)
		obs = t(obs)   
		  
		for (j in 1:M) {
		   	w = matrix(gamma[,j], 1,T-1)
		    wobs = obs[1:(T-1),] * repmat(t(w),1,d*order)
            wobs_1= obs[2:T,] * repmat(t(w),1,d*order)
            if (is.na(sum(obs))) {
            	wobs[is.na(wobs)] = 0
            	wobs_1[is.na(wobs_1)] = 0
            	obs[is.na(obs)] = 0
            }            
            m[,j] = m[,j] + apply(wobs,2,sum)
            m_1[,j] = m_1[,j] + apply(wobs_1, 2,sum)
            op[,,j] = op[,,j] + t(wobs) %*% obs[1:(T-1),]
            op_1[,,j] = op_1[,,j] + t(wobs) %*% obs[2:T,]
            op_2[,,j] = op_2[,,j] + t(wobs_1) %*% obs[2:T,]
         }
     }
        
        # Markov chain
        prior = normalise(exp_num_visits1)
        prior=matrix(prior,M,1)
        transmat = mk_stochastic(exp_num_trans)
        
        if (min(postmix)<1e-6) {stop("error : smoothing probabilities are to small, in one regime at least. You should revise initialisation.")}
        moy <- array(0,c(M,d))
        Sigma <- array(0,c(d,d,M))
		A2 <-array(0,c(M,order,d^2))
				
		if (p>0) {																		
		   for (j in 1:M) { 
			   Cxx = postmix[j]*op[,,j] - m[,j]%*%t(m[,j])
        	   Cxy = postmix[j]*op_1[,,j] - m[,j]%*%t(m_1[,j])
        	   A2tmp = t(Cxy)%*%solve(Cxx+lambda*diag(1,d)) 
        	   tmp = (m_1[,j]-(A2tmp)%*%m[,j])/postmix[j] 
        	   moy[j,1:d] = tmp[1:d] 
        	   op_1[,,j] = t(as.matrix(op_1[,,j]))
        	   tmp2 = (op_2[, , j] + (A2tmp) %*% op[, , j] %*% t(A2tmp) - 
                   ((A2tmp) %*% t(op_1[, , j]) + t((A2tmp) %*% t(op_1[, , j]))))/postmix[j] - tmp %*% t(tmp)
               Sigma[1:d,1:d,j]=tmp2[1:d,1:d]
               for(kp in 1:order){
               	A2[j,kp,] = A2tmp[1:d,((kp-1)*d+1):(kp*d)]
               }
			}

		} else {
			for (j in 1:M) { 
		    	tmp = (m[,j])/postmix[j] 
			    moy[j,1:d] = tmp[1:d] 
			    tmp2 = op[, , j]/postmix[j] - tmp %*% t(tmp)
                Sigma[1:d,1:d,j]=tmp2[1:d,1:d]
			}

		}
		
       if(d>1){
        Atmp=list()
        sigma=list()
        for(j in 1:M){
        	Atmp[[j]]=list()
        	for(kp in 1:order){
        		Atmp[[j]][[kp]]=matrix(A2[j,kp,],d,d)
        	}
        	sigma[[j]]=Sigma[,,j]
        }
        }
        	
		else{
			Atmp=matrix(A2,M,order)
			sigma=matrix(Sigma,byrow=TRUE,nrow=M)
		}
																
    if (p>0) {
	    list(A=Atmp,A0=moy,sigma=sigma,prior=prior,transmat=transmat)
	} else {
		list(sigma=sigma,A0=moy,prior=prior,transmat=transmat)
	}
}