A frequency domain bootstrap for ratio statistics in time series analysis. (English) Zbl 0867.62072

Dahlhaus, R.; Janas, D.

Ann. Stat. 24, No. 5, 1934-1963 (1996).

Summary: The asymptotic properties of the bootstrap in the frequency domain based on Studentized periodogram ordinates are studied. It is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations. By using Edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation. The results carry over to Whittle estimates [P. Whittle, Ark. Mat. 2, 423-434 (1953; Zbl 0053.41003)]. In a simulation study the behavior of the bootstrap is studied for empirical correlations and Whittle estimates.

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20	Asymptotic distribution theory in statistics
62G09	Nonparametric statistical resampling methods

Keywords:

spectral mean; Whittle estimators; bootstrap; frequency domain; Studentized periodogram ordinates; ratio statistics; autocorrelations; Edgeworth expansions

Citations:

Zbl 0053.41003