Weighted discrete ARMA models for categorical time series
Publication date
2024-09-06
Document type
Forschungsartikel
Author
Organisational unit
ISSN
Series or journal
Journal of time series analysis
Peer-reviewed
✅
Part of the university bibliography
✅
Keyword
Discrete ARMA model
Markov chain
Negative serial dependence
Ordinal time series
Qualitative data
Weighting operator
Abstract
A new and flexible class of ARMA-like (autoregressive moving average) models for nominal or ordinal time series is proposed, which are characterized by using so-called weighting operators and are, thus, referred to as weighted discrete ARMA (WDARMA) models. By choosing an appropriate type of weighting operator, one can model, for example, nominal time series with negative serial dependencies, or ordinal time series where transitions to neighboring states are more likely than sudden large jumps. Essential stochastic properties of WDARMA models are derived, such as the existence of a stationary, ergodic, and -mixing solution as well as closed-form formulae for marginal and bivariate probabilities. Numerical illustrations as well as simulation experiments regarding the finite-sample performance of maximum likelihood estimation are presented. The possible benefits of using an appropriate weighting scheme within the WDARMA class are demonstrated by a real-world data application.
Description
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Version
Online first
Access right on openHSU
Metadata only access
Open Access Funding
Wiley (DEAL)