A Frequency Domain Bootstrap for Ratio Statistics in Time Series Analysis

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...

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Veröffentlicht in:	The Annals of statistics 1996-10, Vol.24 (5), p.1934-1963
Hauptverfasser:	Dahlhaus, R., Janas, D.
Format:	Artikel
Sprache:	eng
Schlagworte:	62E20 62M10 Approximation Approximations and expansions Autocorrelation Autocorrelations bootstrap Bootstrap resampling Density estimation Exact sciences and technology Inference from stochastic processes time series analysis Mathematical analysis Mathematical foundations Mathematics periodogram ordinates Probability and statistics ratio statistics Sciences and techniques of general use Spectral energy distribution spectral mean Statistical theories Statistical variance Statistics Time series Time series analysis Whittle estimators
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Zusammenfassung:	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. In a simulation study the behavior of the bootstrap is studied for empirical correlations and Whittle estimates.
ISSN:	0090-5364 2168-8966
DOI:	10.1214/aos/1069362304