ARMA Models

Abstract

In this chapter, we introduce an important parametric family of stationary time series, the autoregressive moving average or ARMA processes. For a large class of autocovariance functions γ (•), it is possible to find an ARMA process {X _t } with ACVF γ _X (·) such that γ(·) is well approximated by γ _X (·). In particular, for any positive integer K, there exists an ARMA process {X _t } such that γ _X (h) = γ(h) for h = 0, 1,.... K. For this (and other) reasons, the family of ARMA processes plays a key role in the modelling of time series data. The linear structure of ARMA processes also leads to a substantial simplification of the general methods for linear prediction discussed earlier in Section 2.5.