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Keywords:

  • Double AR model;
  • non-stationarity;
  • quasi-maximum likelihood estimation

Abstract

This article first studies the non-stationarity of the first-order double AR model, which is defined by the random recurrence equation inline image, where γ0 > 0, α0 ≥ 0, and {ηt}is a sequence of i.i.d. symmetric random variables. It is shown that the double AR(1) model is explosive under the condition inline image. Based on this, it is shown that the quasi-maximum likelihood estimator of (φ0,α0) 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.