Abstract

We consider maximum deviations of sample autocovariances and autocorrelations from their theoretical counterparts. The maximum is taken over a number of lags that increases with the number of observations. For strictly stationary time series the asymptotic distribution of such statistics is of Gumbel type. However speed of convergence to the Gumbel distribution is rather slow. The well-known autoregressive (AR) sieve bootstrap is asymptotically valid for such maximum deviations but suffers from the same slow convergence rate. Braumann et al. 2021 showed that for linear time series the AR sieve bootstrap speed of convergence is of polynomial order. We use the idea of Gaussian approximation for high-dimensional time series to show that for the class of strictly stationary processes a wild-type bootstrap is asymptotically valid for our statistic of interest at a polynomial convergence rate. We close with results from a small simulation study that investigates finite sample properties of mentioned bootstrap proposal.