On non-stationary threshold autoregressive models

TL;DR

This paper investigates the limiting distributions of least-squares estimators in non-stationary first-order threshold autoregressive models, revealing behaviors distinct from classical unit root and explosive AR(1) models.

Contribution

It provides a theoretical analysis of the asymptotic distributions of estimators in non-stationary TAR(1) models, highlighting their unique properties.

Findings

Limiting distributions differ from classical models

Behavior varies significantly in non-stationary regimes

Provides theoretical foundation for inference in TAR models

Abstract

In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).