Estimation of weak ARMA models with regime changes

TL;DR

This paper analyzes the asymptotic properties of least squares estimators for ARMA models with regime changes, relaxing independence assumptions and providing conditions for consistency and normality, supported by Monte Carlo simulations.

Contribution

It extends ARMA regime change models by relaxing error independence, deriving new asymptotic properties, and addressing covariance estimation.

Findings

Conditions for consistency and asymptotic normality established.

Asymptotic covariance matrix can differ significantly from standard models.

Monte Carlo experiments illustrate theoretical results.

Abstract

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of autoregressive moving-average (ARMA) models with regime changes under the assumption that the errors are uncorrelated but not necessarily independent. Relaxing the independence assumption considerably extends the range of application of the class of ARMA models with regime changes. Conditions are given for the consistency and asymptotic normality of the LSE. A particular attention is given to the estimation of the asymptotic covariance matrix, which may be very different from that obtained in the standard framework. The theoretical results are illustrated by means of Monte Carlo experiments.