R/auto.cov.R

In yanyachen/arimaMisc: Time Series Analysis Miscellaneous Tools

#' @title Compute autocovariance function of ARMA process
#'
#' @description
#' Compute autocovariance function of ARMA process.
#'
#' @param ar AR parameters
#' @param ma MA parameters
#' @param sigma2 sigma2
#' @param lag lag
#' @return parameters of autocovariance function
#' @export

auto.cov <- function(ar=0,ma=0,sigma2=1,lag){
  p <- length(ar)
  q <- length(ma)
  m <- max(p,q)+1
  Phi <- array(0,c(m,m))
  phi <- rep(0,m)
  phi[1] <- 1
  phi[1:p+1] <- -ar
  theta <- rep(0,m)
  theta[1] <- 1
  theta[1:q+1] <- ma
  psi <- memory(ar,ma,lag)
  b <- rep(0,m)
  
  Phi[1,] <- phi
  for (i in 2:m){
    Phi[i,1:(m-i+1)] <- phi[i:m]
    Phi[i,2:i] <- Phi[i,2:i] + phi[(i-1):1]
  }
  for (i in 1:m){
    b[i] <- sum(psi[1:(m-i+1)]*theta[i:m])
  }

  gamma <- rep(0,lag+1)
  gamma[1:m] <- solve(Phi)%*%b
  for (k in m:lag){
    gamma[k+1] <- sum(ar*gamma[k:(k-p+1)])
  }
  return(gamma*sigma2)
}