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ARMA Models

2002; Springer International Publishing; Linguagem: Inglês

10.1007/0-387-21657-x_3

2197-4136

Peter J. Brockwell, Richard A. Davis,

Business Process Modeling and Analysis

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 or ARMA processes plays a key role in the modeling of time series data. The linear structured of ARMA processes also leads to a substantial simplification of the general methods for linear prediction discussed earlier in Section 2.5.