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Confidence intervals for spectral mean and ratio statistics

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  • Xiaofeng Shao

Abstract

We propose a new method, to construct confidence intervals for spectral mean and related ratio statistics of a stationary process, that avoids direct estimation of their asymptotic variances. By introducing a bandwidth, a self-normalization procedure is adopted and the distribution of the new statistic is asymptotically nuisance-parameter free. The bandwidth is chosen using information criteria and a moving average sieve approximation. Through a simulation study, we demonstrate good finite sample performance of our method when the sample size is moderate, while a comparison with an empirical likelihood-based method for ratio statistics is made, confirming a wider applicability of our method. Copyright 2009, Oxford University Press.

Suggested Citation

  • Xiaofeng Shao, 2009. "Confidence intervals for spectral mean and ratio statistics," Biometrika, Biometrika Trust, vol. 96(1), pages 107-117.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:107-117
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    File URL: http://hdl.handle.net/10.1093/biomet/asn067
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    Cited by:

    1. Zhang, Xinyu & Tong, Howell, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," LSE Research Online Documents on Economics 113566, London School of Economics and Political Science, LSE Library.
    2. Xinyu Zhang & Howell Tong, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 543-565, April.
    3. Xiaofeng Shao, 2010. "A self‐normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366, June.

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