Non-Stationarity And Quasi-Maximum Likelihood Estimation On A Double Autoregressive Model

type="main" xml:id="jtsa12058-abs-0001"> This article first studies the non-stationarity of the first-order double AR model, which is defined by the random recurrence equation y t = φ 0 y t − 1 + η t γ 0 + α 0 y t − 1 2 , 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 E log &7C φ 0 + η t α 0 &7C > 0 . 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.