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 (⋅ ).
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References
Ansley, C. F. (1979). An algorithm for the exact likelihood of a mixed autoregressive-moving-average process. Biometrika, 66, 59–65.
Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods (2nd ed.). New York: Springer.
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Brockwell, P.J., Davis, R.A. (2016). ARMA Models. In: Introduction to Time Series and Forecasting. Springer Texts in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-29854-2_3
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DOI: https://doi.org/10.1007/978-3-319-29854-2_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-29852-8
Online ISBN: 978-3-319-29854-2
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