adding the iv4 method

1 files changed, 47 insertions, 0 deletions

diff --git a/R/iv.R b/R/iv.R
new file mode 100644
index 0000000..b0f9aff
--- /dev/null
+++ b/R/iv.R
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+#' @export
+iv <- function(z,order=c(0,1,0)){
+  y <- outputData(z); u <- inputData(z); N <- dim(y)[1]
+  na <- order[1];nb <- order[2]; nk <- order[3]
+  nb1 <- nb+nk-1 ; n <- max(na,nb1); df <- N-na-nb
+  
+  # Initial Guess using ARX
+  mod_arx <- arx(z,order)
+  x <- matrix(sim(mod_arx$sys,u,sigma=0))
+  
+  padZeros <- function(x,n) c(rep(0,n),x,rep(0,n))
+  yout <- apply(y,2,padZeros,n=n);
+  xout <- apply(x,2,padZeros,n=n);
+  uout <- apply(u,2,padZeros,n=n);
+  
+  # Regressors
+  reg <- function(i) {
+    if(nk==0) v <- i-0:(nb-1) else v <- i-nk:nb1
+    c(-yout[i-1:na,,drop=T],uout[v,,drop=T])
+  }
+  phi <- t(sapply(n+1:(N+n),reg))
+  Y <- yout[n+1:(N+n),,drop=F]
+  
+  # Generating IVs
+  ivx <- function(i) {
+    if(nk==0) v <- i-0:(nb-1) else v <- i-nk:nb1
+    c(-xout[i-1:na,,drop=T],uout[v,,drop=T])
+  }
+  psi <- t(sapply(n+1:(N+n),ivx))
+  
+  # Estimator
+  lhs <- t(psi)%*%phi; lhsinv <- solve(lhs)
+  theta <- lhsinv%*%t(psi)%*%Y
+  
+  # Residuals
+  ypred <- (phi%*%theta)[1:N,,drop=F] 
+  e <- y-ypred
+  sigma2 <- norm(e,"2")^2/df
+  vcov <- sigma2*solve(t(phi)%*%phi)
+  
+  model <- idpoly(A = c(1,theta[1:na]),B = theta[na+1:nb],
+                  ioDelay = nk,Ts=deltat(z))
+  
+  estpoly(sys = model,
+          stats=list(vcov = vcov, sigma = sqrt(sigma2),df = df),
+          fitted.values=ypred,residuals=e,call=match.call(),input=u)
+}
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