B1843
Title: Bootstrap convergence rates for the max of an increasing number of autocovariances and -correlations under stationarity
Authors: Alexander Braumann - TU Braunschweig (Germany) [presenting]
Jens-Peter Kreiss - Technische Universitaet Braunschweig (Germany)
Marco Meyer - TU Braunschweig (Germany)
Abstract: Maximum deviations of sample autocovariances and autocorrelations are considered from their theoretical counterparts over a number of lags that increase with the number of observations. The asymptotic distribution of such statistics e.g. for strictly stationary time series is of Gumbel type. However, the 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. A past study showed that for linear time series, the AR sieve bootstrap speed of convergence is of polynomial order. The idea of Gaussian approximation is used to show that for the class of strictly stationary processes, a hybrid variant of the AR sieve bootstrap is asymptotically valid for the statistic of interest at a polynomial convergence rate. Results from a small simulation study that investigates finite sample properties of the mentioned bootstrap proposals are concluded.
