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Entropy Measures for Data Analysis: Theory, Algorithms and Applications
Open AccessArticle

Regime-Switching Discrete ARMA Models for Categorical Time Series

Department of Mathematics and Statistics, Helmut Schmidt University, 22043 Hamburg, Germany
Entropy 2020, 22(4), 458; https://doi.org/10.3390/e22040458
Received: 18 March 2020 / Revised: 14 April 2020 / Accepted: 16 April 2020 / Published: 17 April 2020
For the modeling of categorical time series, both nominal or ordinal time series, an extension of the basic discrete autoregressive moving-average (ARMA) models is proposed. It uses an observation-driven regime-switching mechanism, leading to the family of RS-DARMA models. After having discussed the stochastic properties of RS-DARMA models in general, we focus on the particular case of the first-order RS-DAR model. This RS-DAR ( 1 ) model constitutes a parsimoniously parameterized type of Markov chain, which has an easy-to-interpret data-generating mechanism and may also handle negative forms of serial dependence. Approaches for model fitting are elaborated on, and they are illustrated by two real-data examples: the modeling of a nominal sequence from biology, and of an ordinal time series regarding cloudiness. For future research, one might use the RS-DAR ( 1 ) model for constructing parsimonious advanced models, and one might adapt techniques for smoother regime transitions. View Full-Text
Keywords: categorical time series; discrete ARMA models; parsimonious Markov chain; regime-switching models categorical time series; discrete ARMA models; parsimonious Markov chain; regime-switching models
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Weiß, C.H. Regime-Switching Discrete ARMA Models for Categorical Time Series. Entropy 2020, 22, 458.

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