The Annals of Statistics

A frequency domain bootstrap for ratio statistics in time series analysis

R. Dahlhaus and D. Janas

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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

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

First available in Project Euclid: 20 November 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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