Recursive Least Squares with Exponential Forgetting

RLSEF.R

RLSF <- function(y,x,alpha=0.95,ist=30,xpxi=NULL,xpy0=NULL)
{
  # http://queue.acm.org/detail.cfm?id=2534976
  if(!is.matrix(x))x=as.matrix(x)
  nT=dim(x)[1]
  k=dim(x)[2]
  xpx0 = NULL
  #
  if(is.null(xpxi)){
    if(ist <= k)ist=k+1
    xpx0=t(x[1:ist,])%*%x[1:ist,]
    xpxi=solve(xpx0)
    xpy0=t(x[1:ist,])%*%matrix(y[1:ist],ist,1)
  }
  
  ist=ist+1
  resi=NULL
  beta=matrix(c(xpxi%*%xpy0),1,k)
  for (t in ist:nT){
    jdx=t-ist+1
    x1=matrix(x[t,],1,k)
    tx1 = t(x1)
    xpx0 = alpha * xpx0 + tx1 %*% x1
    xpy0 = alpha * xpy0 + tx1 * y[[t]]
    xpxi=solve(xpx0)
    tmp = matrix(c(xpxi%*%xpy0),1,k)
    beta=rbind(beta,tmp)
    res=y[t]-tmp%*%t(x1)
    resi=c(resi,res)
  }
  beta=beta[-1,]
  
  RLSF <- list(beta=beta,resi=resi)
}