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#' Estimate Impulse Response Models
#'
#' \code{impulseest} is used to estimate impulse response models in the
#' given data
#'
#' @param data an object of class \code{idframe}
#' @param M Order of the FIR Model (Default:\code{30})
#' @param K Transport delay in the estimated impulse response
#' (Default:\code{0})
#'
#' @seealso \code{\link{step}}
#'
#' @examples
#' uk <- rnorm(1000,1)
#' yk <- filter (uk,c(0.9,-0.4),method="recursive") + rnorm(1000,1)
#' data <- idframe(output=data.frame(yk),input=data.frame(uk))
#' fit <- impulseest(data)
#' plot(fit)
#'
#' @export
impulseest <- function(data,M=30,K=0){
N <- dim(data$output)[1]
ind <- (M+K+1):N
z_reg <- function(i) data$input[(i-K):(i-M-K),]
Z <- t(sapply(ind,z_reg))
Y <- data$output[ind,]
# Fit Linear Model and find standard errors
fit <- lm(Y~Z-1)
df <- nrow(Z)-ncol(Z);sigma2 <- sum(resid(fit)^2)/df
vcov <- sigma2 * solve(t(Z)%*%Z)
se <- sqrt(diag(vcov))
out <- list(coefficients=coef(fit),residuals=resid(fit),lags=K:(M+K),
x=colnames(data$input),y=colnames(data$output),se = se)
class(out) <- "impulseest"
return(out)
}
#' Impulse Response Plots
#'
#' Plots the estimated IR Coefficients
#'
#' @param model an object of class \code{impulseest}
#' @param sig Significance Limits (Default: \code{0.975})
#'
#' @seealso \code{\link{impulseest}},\code{\link{step}}
#' @export
plot.impulseest <- function(model,sig=0.975){
lim <- model$se*qnorm(0.975)
ylim <- c(min(coef(model)),max(coef(model)))
title <- paste("Impulse Response \n From",model$x,"to",model$y)
plot(model$lags,coef(model),type="h",xlab="Lag",ylab= model$y,
main = title)
abline(h=0);points(x=model$lags,y=lim,col="blue",lty=2,type="l")
points(x=model$lags,y=-lim,col="blue",lty=2,type="l")
}
#' Step Response Plots
#'
#' Plots the step response of a system, given the IR model
#'
#' @param model an object of class \code{impulseest}
#'
#' @seealso \code{\link{impulseest}}
#' @export
step <- function(model){
title <- paste("Step Response \n From",model$x,"to",model$y)
stepResp <- cumsum(coef(model))
plot(model$lags,stepResp,type="s",xlab="Lag",ylab= model$y,
main = title)
abline(h=0)
}
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