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The ARMA alphabet soup: A tour of ARMA model variants

Author(s): Scott H. Holan | Robert Lund | Ginger Davis

Journal: Statistics Surveys
ISSN 1935-7516

Volume: 4;
Start page: 232;
Date: 2010;
Original page

Keywords: Autocovariance function | Counts | Long memory | Short memory | Stochastic volatility | Time series

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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