Open Access
2010 The ARMA alphabet soup: A tour of ARMA model variants
Scott H. Holan, Robert Lund, Ginger Davis
Statist. Surv. 4: 232-274 (2010). DOI: 10.1214/09-SS060


Autoregressive moving-average (ARMA) difference equations are ubiquitous models for short memory time series and have parsimoniously described many stationary series. Variants of ARMA models have been proposed to describe more exotic series features such as long memory autocovariances, periodic autocovariances, and count support set structures. This review paper enumerates, compares, and contrasts the common variants of ARMA models in today’s literature. After the basic properties of ARMA models are reviewed, we tour ARMA variants that describe seasonal features, long memory behavior, multivariate series, changing variances (stochastic volatility) and integer counts. A list of ARMA variant acronyms is provided.


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Scott H. Holan. Robert Lund. Ginger Davis. "The ARMA alphabet soup: A tour of ARMA model variants." Statist. Surv. 4 232 - 274, 2010.


Published: 2010
First available in Project Euclid: 7 December 2010

zbMATH: 1274.62594
MathSciNet: MR2748178
Digital Object Identifier: 10.1214/09-SS060

Primary: 62M10
Secondary: 91B84

Keywords: Autocovariance function , counts , long memory , short memory , stochastic volatility , time series

Rights: Copyright © 2010 The author, under a Creative Commons Attribution License

Vol.4 • 2010
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