Soft-clipping autoregressive models for ordinal time series
Publication date
2025-05-01
Document type
Forschungsartikel
Author
Organisational unit
Scopus ID
Publisher
Wiley
Series or journal
Applied Stochastic Models in Business and Industry
ISSN
Periodical volume
41
Periodical issue
3
Article ID
e70015
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Conditional regression model
Linear models
Ordinal time series
Soft-clipping link
Abstract
The linear autoregressive models are among the most popular models in the practice of time series analysis, which constitutes an incentive to adapt them to ordinal time series as well. Our starting point for modeling ordinal time series data is the latent variable approach to define a generalized linear model. This method, however, typically leads to a non-linear relationship between the past observations and the current conditional cumulative distribution function (cdf). To overcome this problem, we use the soft-clipping link to obtain an approximately linear model structure and propose a wide and flexible class of soft-clipping autoregressive (scAR) models. The constraints imposed on the model parameters allow us to identify relevant special cases of the scAR model family. We study the calculation of transition probabilities as well as approximate formulae for the CDF. Our proposals are illustrated by numerical examples and simulation experiments, where the performance of maximum likelihood estimation as well as model selection is analyzed. The novel model family is successfully applied to a real-world ordinal time series from finance.
Description
This is an open access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
Version
Published version
Access right on openHSU
Metadata only access