Estimation in threshold autoregressive models with correlated innovations

TL;DR

This paper analyzes the asymptotic distribution of the Bayes estimator in threshold autoregressive models driven by correlated Gaussian noise, extending traditional uncorrelated noise assumptions.

Contribution

It provides a complete characterization of the asymptotic distribution of the Bayes estimator under correlated Gaussian innovations in TAR models.

Findings

Asymptotic distribution derived for correlated Gaussian noise

Extension of TAR model analysis to correlated innovations

Theoretical framework for Bayesian estimation in TAR models

Abstract

Large sample statistical analysis of threshold autoregressive (TAR) models is usually based on the assumption that the underlying driving noise is uncorrelated. In this paper, we consider a model, driven by Gaussian noise with geometric correlation tail and derive a complete characterization of the asymptotic distribution for the Bayes estimator of the threshold parameter.