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Wavelet variance analysis for gappy time series

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Abstract

The wavelet variance is a scale-based decomposition of the process variance for a time series and has been used to analyze, for example, time deviations in atomic clocks, variations in soil properties in agricultural plots, accumulation of snow fields in the polar regions and marine atmospheric boundary layer turbulence. We propose two new unbiased estimators of the wavelet variance when the observed time series is ‘gappy,’ i.e., is sampled at regular intervals, but certain observations are missing. We deduce the large sample properties of these estimators and discuss methods for determining an approximate confidence interval for the wavelet variance. We apply our proposed methodology to series of gappy observations related to atmospheric pressure data and Nile River minima.

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Authors and Affiliations

  1. Department of Statistics, University of Chicago, 5734 South University Avenue, Chicago, IL, 60637, USA

    Debashis Mondal

  2. Applied Physics Laboratory, University of Washington, Box 355640, Seattle, WA, 98195, USA

    Donald B. Percival

Authors
  1. Debashis Mondal
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  2. Donald B. Percival
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Corresponding author

Correspondence to Debashis Mondal.

Additional information

Supported by NSF Grant DMS-02-22115.

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Mondal, D., Percival, D.B. Wavelet variance analysis for gappy time series. Ann Inst Stat Math 62, 943–966 (2010). https://doi.org/10.1007/s10463-008-0195-z

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  • DOI: https://doi.org/10.1007/s10463-008-0195-z

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