The Annals of Statistics

A frequency domain bootstrap for ratio statistics in time series analysis

R. Dahlhaus and D. Janas

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Abstract

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.

Article information

Source
Ann. Statist. Volume 24, Number 5 (1996), 1934-1963.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
http://projecteuclid.org/euclid.aos/1069362304

Mathematical Reviews number (MathSciNet)
MR1421155

Digital Object Identifier
doi:10.1214/aos/1069362304

Zentralblatt MATH identifier
0867.62072

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62E20: Asymptotic distribution theory

Keywords
Autocorrelations bootstrap periodogram ordinates ratio statistics spectral mean time series Whittle estimators

Citation

Dahlhaus, R.; Janas, D. A frequency domain bootstrap for ratio statistics in time series analysis. Ann. Statist. 24 (1996), no. 5, 1934--1963. doi:10.1214/aos/1069362304. http://projecteuclid.org/euclid.aos/1069362304.


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