A New Method for Obtaining the Autocovariance of an ARMA Model_ An Exact Form Solution

M. KARANASOS
York University
In this article we present a new method for computing the theoretical autocovariance
function of an autoregressive moving average model. The importance of our
theorem is that it yields two interesting results: First, a closed-form solution is
derived in terms of the roots of the autoregressive polynomial and the parameters of
the moving average part. Second, a sufficient condition for the lack of model redundancy
is obtained.
1, INTRODUCTION
In this paper we present a new method for computing the theoretical autocovariance
function of an autoregressive moving average (ARMA) model.
In Section 2 of this paper we give a new method for computing the theoretical
autocovariance function of an autoregressive (AR) scheme. Exact methods of
calculating the autocovariance for autoregressive models are given by Quenouille
(1947) and Pagano (1973). We believe that our method is an improvement
over those proposed by Quenouille and Pagano. It is exact, easily coded, and can
be used for AR models of all orders.