Abstract: A buffered autoregression extends the classical threshold autoregression by allowing a buffer region for regime changes. In this study, we examine asymptotic statistical inferences for the two-regime buffered autoregressive (BAR) model, with autoregressive unit roots. We propose a Sup-LR test for the nonlinear buffer effect in the possible presence of unit roots, and a class of unit root tests to identify the number of nonstationary regimes in the BAR model. The wild bootstrap method is suggested to approximate the critical values of the two tests. Simulation results show that the proposed unit root test outperforms the conventional augmented Dickey-Fuller test, and that the two wild bootstrap tests are robust to unknown heteroscedasticity. Two macroeconomic data examples, based on U.S. unemployment rates and real exchange rates, respectively, are provided to illustrate the methods.

Key words and phrases: Asymptotic theory, buffer effect, nonlinear time series, nonstationary, threshold autoregression, wild bootstrap.