Statistics Surveys

The ARMA alphabet soup: A tour of ARMA model variants

Scott H. Holan, Robert Lund, and Ginger Davis

Full-text: Open access

Abstract

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.

Article information

Source
Statist. Surv. Volume 4 (2010), 232-274.

Dates
First available in Project Euclid: 7 December 2010

Permanent link to this document
http://projecteuclid.org/euclid.ssu/1291731822

Digital Object Identifier
doi:10.1214/09-SS060

Zentralblatt MATH identifier
06162225

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 91B84: Economic time series analysis [See also 62M10]

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

Citation

Holan, Scott H.; Lund, Robert; Davis, Ginger. The ARMA alphabet soup: A tour of ARMA model variants. Statist. Surv. 4 (2010), 232--274. doi:10.1214/09-SS060. http://projecteuclid.org/euclid.ssu/1291731822.


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