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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, A07103, doi:10.1029/2005JA011233, 2006

Statistical bias in periodograms derived from solar wind time series

J. J. Podesta

Laboratory for Solar and Space Physics, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA

Abstract

The bias in periodogram spectral estimators is computed as a function of the sample size N by assuming a model power spectrum that decays like f ^−α at high frequencies. For α = 2, it is shown that when the aliasing of the measured power spectrum is properly taken into account the bias in the “raw” periodogram is nearly independent of frequency for large N. For the range of values 1.7 α <2, an upper bound on the bias is provided by the case α = 2. Theoretical calculations of the maximum absolute bias as a function of N are used to determine when the periodogram is approximately unbiased and when the bias is significant enough to require the use of a modified periodogram which incorporates data tapering, also called data windowing. For solar wind velocity data acquired by the ACE spacecraft and a chosen low frequency cutoff of 10⁻⁷ Hz, the bias in periodogram spectral estimators is found to be less than 4% for sample sizes N greater than 2¹⁶ = 65536. This corresponds to a 49 day record of 64 s data.

Received 16 May 2005; accepted 13 March 2006; published 19 July 2006.

Keywords: power spectra; solar wind; spectral estimation.

Index Terms: 3255 Mathematical Geophysics: Spectral analysis (3205, 3280); 2164 Interplanetary Physics: Solar wind plasma; 3265 Mathematical Geophysics: Stochastic processes (3235, 4468, 4475, 7857); 3270 Mathematical Geophysics: Time series analysis (1872, 4277, 4475).

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Citation: Podesta, J. J. (2006), Statistical bias in periodograms derived from solar wind time series, J. Geophys. Res., 111, A07103, doi:10.1029/2005JA011233.

Copyright 2006 by the American Geophysical Union.