NON‐STATIONARITY AND QUASI‐MAXIMUM LIKELIHOOD ESTIMATION ON A DOUBLE AUTOREGRESSIVE MODEL

Abstract

Abstract This article first studies the non‐stationarity of the first‐order double AR model, which is defined by the random recurrence equation , where γ 0 > 0, α 0 ≥ 0, and { η t }is a sequence of i.i.d. symmetric random variables. It is shown that the double AR(1) model is explosive under the condition . Based on this, it is shown that the quasi‐maximum likelihood estimator of ( φ 0 , α 0 ) is consistent and asymptotically normal so that the unit root problem does not exist in the double AR(1) model. Simulation studies are carried out to assess the performance of the quasi‐maximum likelihood estimator in finite samples.