Bayesian estimation of a multivariate TAR model when the noise process distribution belongs to the class of Gaussian variance mixtures

L.H. Vanegas, S.A. Calderón V and L.M. Rondón

International Journal of Forecasting, 2026, vol. 42, issue 2, 492-511

Abstract: Threshold autoregressive (TAR) models are powerful tools for analyzing nonlinear and multivariate time series, which include Multivariate Self-Exciting Threshold Autoregressive (MSETAR) and Vector Autoregressive (VAR) models as special cases. In this paper, parameter estimation, inference, and forecasting are developed for multivariate TAR (MTAR) models using the Bayesian approach in a flexible setup, under which not only the Gaussian distribution but also the other distributions that belong to the class of Gaussian variance mixtures can be used to describe the noise process behavior. That class of distributions includes Student-t, Slash, symmetric hyperbolic, and contaminated normal, which are also symmetric but more flexible and have heavier tails than the Gaussian one. Inferences from MTAR models based on that kind of distribution may be less affected by extreme or outlying observations than those based on the Gaussian distribution. All parameters in the MTAR model are included in the proposed MCMC-type algorithm, except the number of regimes and the autoregressive orders, which can be chosen using Deviance Information Criterion (DIC) and/or Watanabe-Akaike Information Criterion (WAIC) and/or Root Mean Square Error (RMSE) and/or log-score. A library for the language and environment for statistical computing R was developed to assess the effectiveness of the proposed methodology using simulation studies and analysis of a real multivariate time series.

Keywords: Multivariate threshold autoregressive model; Bayesian analysis; Forecasting; Gaussian variance mixtures distribution; Non-linear time series (search for similar items in EconPapers)
Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016920702500069X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:intfor:v:42:y:2026:i:2:p:492-511

DOI: 10.1016/j.ijforecast.2025.08.001

Access Statistics for this article

International Journal of Forecasting is currently edited by R. J. Hyndman

More articles in International Journal of Forecasting from Elsevier
Bibliographic data for series maintained by Catherine Liu ().