Computing the asymptotic covariance matrix of a vector of sample autocorrelations for ARMA processes

摘要

An autoregressive moving average (ARMA) process driven by a sequence of independent and identically distributed random variables is considered. In this context, it is shown that the analytical Barlett's formula for the asymptotic covariance matrix of a vector of sample autocorrelations reduces to a matrix product where the factors involved can be determined by performing a finite number of algebraic operations.