Nonlinear GARCH-type models for ordinal time series
Publication date
2023-10-21
Document type
Forschungsartikel
Author
Organisational unit
ISSN
Series or journal
Stochastic environmental research and risk assessment
Periodical volume
38
Periodical issue
2
First page
637
Last page
649
Peer-reviewed
✅
Part of the university bibliography
✅
Keyword
Artificial neural networks
Logit model
Nonlinear regression
Ordinal time series
Softmax function
Abstract
Despite their relevance in various areas of application, only few stochastic models for ordinal time series are discussed in the literature. To allow for a flexible serial dependence structure, different ordinal GARCH-type models are proposed, which can handle nonlinear dependence as well as kinds of an intensified memory. The (logistic) ordinal GARCH model accounts for the natural order among the categories by relying on the conditional cumulative distributions. As an alternative, a conditionally multinomial model is developed which uses the softmax response function. The resulting softmax GARCH model incorporates the ordinal information by considering the past (expected) categories. It is shown that this latter model is easily combined with an artificial neural network response function. This introduces great flexibility into the resulting neural softmax GARCH model, which turns out to be beneficial in three real-world time series applications (air quality levels, fear states, cloud coverage).
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
Published version
Access right on openHSU
Metadata only access
Open Access Funding
Springer Nature (DEAL)