Abstract
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 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 model for constructing parsimonious advanced models, and one might adapt techniques for smoother regime transitions.
Highlights
Since the pioneering textbook on time series analysis by Box & Jenkins [1], this topic has attracted an immense interest in research and applications
Well-known examples regarding (2) are the so-called mixture transition distribution (MTD) model proposed by Raftery [23], which extends an underlying Markov chain (MC) to a higher-order Markov model with only one additional parameter for each increment of the model order, or the hidden-Markov model (HMM), where the observable process is controlled by a latent
We extended the basic discrete autoregressive moving-average (ARMA) model of Jacobs & Lewis [15] by an observation-driven regime-switching mechanism, leading to the family of RS-DARMA models
Summary
Since the pioneering textbook on time series analysis by Box & Jenkins [1], this topic has attracted an immense interest in research and applications. A large number of models have been developed for this type of discrete data, integer-valued counterparts to the basic ARMA model, and to more advanced models like the aforementioned SETAR models. The latter include the proposals by Möller [6], Möller et al [7], Monteiro et al [8], Thyregod et al [9], Wang et al [10]. As a compromise between flexibility and parsimony, we extend the discrete ARMA models for categorical time series by an observation-driven regime-switching mechanism, see Section 3.
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