A Double AR Model Without Intercept: an Alternative to Modeling Nonstationarity and Heteroscedasticity

TL;DR

This paper introduces the DARWIN model, a non-stationary, heteroskedastic double AR model without intercept, along with estimators and tests for stability, supported by simulations and empirical analysis.

Contribution

It proposes the DARWIN model as an alternative approach to modeling non-stationary heteroskedastic time series, with new estimators and stability tests.

Findings

The DARWIN model is always non-stationary and heteroskedastic.

The Lyapunov exponent estimator is unbiased, consistent, and asymptotically normal.

The QMLE for DARWIN is strongly consistent and asymptotically normal.

Abstract

This paper presents a double AR model without intercept (DARWIN model) and provides us a new way to study the non-stationary heteroskedastic time series. It is shown that the DARWIN model is always non-stationary and heteroskedastic, and its sample properties depends on the Lyapunov exponent. An easy-to-implement estimator is proposed for the Lyapunov exponent, and it is unbiased, strongly consistent and asymptotically normal. Based on this estimator, a powerful test is constructed for testing the stability of the model. Moreover, this paper proposes the quasi-maximum likelihood estimator (QMLE) for the DARWIN model, which has an explicit form. The strong consistency and asymptotical normality of the QMLE are established regardless of the sign of the Lyapunov exponent. Simulation studies are conducted to assess the performance of the estimation and testing and an empirical example is given for illustrating the usefulness of the DARWIN model.