Extending the Range of Validity of the Autoregressive (Sieve) Bootstrap

Abstract

Two modifications of the autoregressive‐sieve and of the autoregressive bootstrap are proposed. The first modification replaces the classical i.i.d. resampling scheme applied to the residuals of the autoregressive fit by the generation of i.i.d. wild pseudo‐innovations that appropriately mimic to the appropriate extent, also the fourth‐order moment structure of the true innovations driving the underlying linear process. This modification extends the validity of the autoregressive‐sieve bootstrap to classes of statistics for which the classical residual‐based autoregressive‐sieve bootstrap fails. In the second modification, an autoregressive bootstrap applied to an appropriately transformed time series is proposed, which, together with a dependent wild‐type generation of pseudo‐innovations, delivers a bootstrap procedure that is valid for large classes of statistics and for stochastic processes satisfying quite general, weak, dependent conditions. A fully data‐driven selection of the bootstrap parameters involved in both modifications is proposed, and extensive simulations, including comparisons with alternative bootstrap methods, show a good finite sample performance of the proposed bootstrap procedures.