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.