On Parameter Estimation of Threshold Autoregressive Models

TL;DR

This paper investigates the Bayesian estimation of threshold parameters in TAR models with random thresholds, establishing consistency, limit distribution, and convergence of moments, supported by simulations for inference.

Contribution

It introduces a Bayesian approach for threshold estimation in TAR models with random thresholds, providing theoretical properties and simulation-based inference methods.

Findings

Bayesian estimator is consistent for threshold parameters.

Limit distribution expressed via a limit likelihood ratio.

Convergence of moments of estimators is proven.

Abstract

This paper studies the threshold estimation of a TAR model when the underlying threshold parameter is a random variable. It is shown that the Bayesian estimator is consistent and its limit distribution is expressed in terms of a limit likelihood ratio. Furthermore, convergence of moments of the estimators is also established. The limit distribution can be computed via explicit simulations from which testing and inference for the threshold parameter can be conducted. The obtained results are illustrated with numerical simulations.