Abstract
In this chapter we introduce an extremely important class of time series {X t , t = 0, ± 1, ± 2,...} defined in terms of linear difference equations with constant coefficients. The imposition of this additional structure defines a parametric family of stationary processes, the autoregressive moving average or ARMA processes. For any autocovariance function γ(·) such that lim h→∞ γ(h) = 0, and for any integer k > 0, it is possible to find an ARMA process with autocovariance function γx(·) such that γx(h) = γ(h), 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 leads also to a very simple theory of linear prediction which is discussed in detail in Chapter 5.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer Science+Business Media New York
About this chapter
Cite this chapter
Brockwell, P.J., Davis, R.A. (1987). Stationary ARMA Processes. In: Time Series: Theory and Methods. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-0004-3_3
Download citation
DOI: https://doi.org/10.1007/978-1-4899-0004-3_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4899-0006-7
Online ISBN: 978-1-4899-0004-3
eBook Packages: Springer Book Archive