Bootstrapping General First Order Autoregression

In this paper we consider general rst order autoregression, including the stationary, the explosive and the unstable case. It is well-known in the literature that the usual bootstrap method for the least squares parameter estimator is asymptotically consistent for the stationary and the explosive case, but does not work in the unstable case, where the parameter value is equal to + 1 or {1. We propose a modiied bootstrap method, which turns out to be asymptotically consistent in all possible situations. Additionally we derive tests for stationarity and nonstationarity for rst order autoregressions. The bootstrap method is used to obtain critical values. Some simulation results are also enclosed.