Bootstrap prediction intervals for SETAR models

This paper considers four methods for obtaining bootstrap prediction intervals (BPIs) for the self-exciting threshold autoregressive (SETAR) model. Method 1 ignores the sampling variability of the threshold parameter estimator. Method 2 corrects the finite sample biases of the autoregressive coefficient estimators before constructing BPIs. Method 3 takes into account the sampling variability of both the autoregressive coefficient estimators and the threshold parameter estimator. Method 4 resamples the residuals in each regime separately. A Monte Carlo experiment shows that (1) accounting for the sampling variability of the threshold parameter estimator is necessary, despite its super-consistency; (2) correcting the small-sample biases of the autoregressive parameter estimators improves the small-sample properties of bootstrap prediction intervals under certain circumstances; and (3) the two-sample bootstrap can improve the long-term forecasts when the error terms are regime-dependent.