Asymptotic distributions related to mildly-explosive second order autoregressive models

TL;DR

This paper investigates the asymptotic behavior of the least squares estimator in mildly-explosive autoregressive models with dependent errors, revealing a Cauchy limit law and implications for near-integrated processes.

Contribution

It introduces a novel limit law for the estimator in mildly-explosive AR(1) models with dependent errors, bridging existing asymptotic theories.

Findings

Estimator has a Cauchy limit law

Results connect moderate deviations with local to unity models

Simulation studies validate finite-sample performance

Abstract

In this paper, we consider the normalized least squares estimator of the parameter in a mildly-explosive first-order autoregressive model with dependent errors which are modeled as a mildly-explosive AR(1) process. We prove that the estimator has a Cauchy limit law which provides a bridge between moderate deviation asymptotics and the earlier results on the local to unity and explosive autoregressive models. In particular, the results can be applied to understand the near-integrated second order autoregressive processes. Simulation studies are also carried out to assess the performance of least squares estimation in finite samples.