Nº 20-01: A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which the method is valid. We show the asymptotic re finements of the proposed procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the advantages of our procedure for Generalized Empirical Likelihood estimation. As a by-product, our fast bootstrap provides higher-order correct asymptotic confi dence distributions. Monte Carlo simulations on an autoregressive conditional duration model provide numerical evidence that the novel bootstrap yields higher-order accurate confi dence intervals. A real-data application on dynamics of trading volume of stocks illustrates the advantage of our method over the routinely-applied fi rst-order asymptotic theory, when the underlying distribution of the test statistic is skewed or fat-tailed.