THE BLOCKWISE BOOTSTRAP FOR GENERAL PARAMETERS OF A STATIONARY TIME-SERIES

We study the blockwise bootstrap of Kunsch (1989) for a statistic whic h estimates a parameter of the entire distribution of a stationary tim e series. Because such a statistic is not symmetric in the observation s, one should not simply resample blocks of the original data. When th e parameter is the spectral distribution function or an ARMA parameter , the statistic is a symmetric function of all shifts of the sample ex tended suitably. Then we can resample blocks of shift indices, and the theory is basically the same as for a symmetric statistic. In other c ases the statistic is a symmetric function of m-tuples of consecutive data where m increases with sample size. Then one can resample blocks of these m-tuples. But the increasing m makes the theory more delicate . We show validity of the bootstrap in two generic examples of spectra l estimators, thereby extending results of Politis and Romano (1992).