Beyond Equidistant Assumptions: An Autoregressive Ordered Stereotype Model for Ordinal Time Series

2026-06-29

AI Summary

This study addresses the limitation of the equidistant assumption commonly imposed in modeling ordinal time series data by proposing an autoregressive ordered stereotype model (AR-OSM). Building upon the ordered stereotype model (OSM) framework, the method incorporates lagged response variables as covariates to effectively capture temporal dependencies while relaxing the restrictive equidistance assumption, thereby allowing data-driven estimation of non-uniform spacings between ordinal categories. Model parameters are inferred via maximum likelihood estimation. Application to infant sleep state data demonstrates the model’s ability to accurately capture underlying temporal structures, and simulation studies confirm its robustness and precision across varying sample sizes and parameter configurations. The proposed approach substantially enhances both the applicability and interpretability of modeling non-equidistant ordinal time series.

Abstract

We propose an extension of the ordered stereotype model (OSM) for ordinal time series data, referred to as the Autoregressive OSM (AR-OSM). The model captures serial dependence by incorporating lagged values of the response as covariates in the systematic component. In contrast to existing regression models for ordinal time series, the AR-OSM does not assume equidistant categories, but instead allows the data to determine their relative spacing. This property makes the model particularly suitable for applications where the equidistance assumption is unrealistic. Such a case is illustrated through the analysis of infant sleep state data. Additionally, a comprehensive simulation study is conducted to assess the performance of the model under varying sample sizes and to investigate how parameter values influence the induced serial dependence structure.

Problem

• ordinal time series
• equidistant assumption
• serial dependence
• ordered stereotype model

Innovation

• Autoregressive OSM
• ordinal time series
• non-equidistant categories
• serial dependence
• ordered stereotype model