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#' Estimate ARX Models
#'
#' @export
estARX <- function(data,order=c(0,1,0)){
y <- as.matrix(data$output)
u <- as.matrix(data$input); N <- dim(y)[1]
na <- order[1];nb <- order[2]; nk <- order[3]
nb1 <- nb+nk; n <- max(na,nb1); df <- N - na - nb -nk
padZeros <- function(x,n) c(rep(0,n),x,rep(0,n))
yout <- apply(y,2,padZeros,n=n);
uout <- apply(u,2,padZeros,n=n);
reg <- function(i) cbind(-yout[i-1:na,],uout[i-nk:nb1])
X <- t(sapply(n+1:(N+n),reg))
Y <- yout[n+1:(N+n),,drop=F]
qx <- qr(X); coef <- qr.solve(qx,Y)
sigma2 <- sum((Y-X%*%coef)^2)/df
vcov <- sigma2 * chol2inv(qx$qr)
model <- arx(A = c(1,coef[1:na]),B = coef[na+1:nb1],ioDelay = nk)
est <- list(coefficients = model,vcov = vcov, sigma = sqrt(sigma2),
df = df,fitted.values=(X%*%coef)[1:N,],
residuals=(Y-X%*%coef)[1:N,],call=match.call())
class(est) <- c("estARX","estPoly")
est
}
#' @export
summary.estARX <- function(object)
{
coefs <- c(coef(object)$A[-1],coef(object)$B)
se <- sqrt(diag(object$vcov))
tval <- coefs / se
TAB <- cbind(Estimate = coefs,
StdErr = se,
t.value = tval,
p.value = 2*pt(-abs(tval), df=object$df))
na <- length(coef(object)$A) - 1; nk <- coef(object)$ioDelay;
nb <- length(coef(object)$B) - nk
rownames(TAB) <- rep("a",nrow(TAB))
for(i in 1:na) rownames(TAB)[i] <- paste("a",i,sep="")
for(j in (na+1):nrow(TAB)) {
rownames(TAB)[j] <- paste("b",j-na-1+nk,sep="")
}
res <- list(call=object$call,coefficients=TAB,sigma=object$sigma,
df=object$df)
class(res) <- "summary.estARX"
res
}
#' @export
print.summary.estARX <- function(object){
cat("Discrete-time ARX model: A(q^{-1})y[k] = B(q^{-1})u[k] + e[k] \n")
cat("Call: ");print(object$call);cat("\n\n")
print(coef(object))
cat(paste("\nsigma:",format(object$sigma,digits=4)))
cat(paste("\nDoF:",object$df))
}
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