Regime-Switching Discrete ARMA Models for Categorical Time Series

Area of Science:

• Statistics
• Time Series Analysis
• Stochastic Processes

Background:

• Traditional discrete autoregressive moving-average (ARMA) models have limitations in modeling complex categorical time series.
• Categorical time series, including nominal and ordinal data, require specialized modeling techniques.
• Existing models may not adequately capture regime-switching dynamics or negative serial dependence.

Purpose of the Study:

• To propose an extension of discrete ARMA models for categorical time series analysis.
• To introduce the family of regime-switching discrete autoregressive moving-average (RS-DARMA) models.
• To present and analyze the first-order regime-switching discrete autoregressive (RS-DAR(1)) model.

Main Methods:

• Development of observation-driven regime-switching mechanisms for discrete time series.
• Stochastic properties analysis of the general RS-DARMA models.
• Focus on the parsimonious parameterization and data-generating mechanism of the RS-DAR(1) model.
• Elaboration of model fitting approaches.

Main Results:

• The proposed RS-DARMA models effectively extend discrete ARMA for categorical time series.
• The RS-DAR(1) model is presented as a parsimonious Markov chain with interpretable data generation.
• The model's capability to handle negative serial dependence is highlighted.
• Successful application of model fitting approaches to real-world nominal (biology) and ordinal (cloudiness) time series data.

Conclusions:

• The RS-DARMA family, particularly the RS-DAR(1) model, provides a flexible and interpretable framework for categorical time series.
• The model demonstrates utility in diverse fields, including biology and meteorology.
• Future research directions include developing advanced parsimonious models and exploring smoother regime transition techniques.