Autocorrelation function and power spectrum for detrended measurements.

Details Autocorrelation function and power spectrum for detrended measurements. Autocorrelation function and power spectrum for detrended measurements.

Apr 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997kfnt...13b..78l&link_type=abstract

Kinematika Fiz. Nebesn. Tel, Tom 13, No. 2, p. 78 - 95

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Methods Of Reduction

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The removal of polynomial trend from random value measurements in case of a limited run length T leads to essential bias of the sample autocorrelation function R(τ) and the spectral density G(f). The precise expressions for computing a dispersion of R(τ) and G(f) using unbiased spectral density g(f) are given for trend orders 0, 1, ..., n. It is shown that for g(f) ∝ f-p the form of a normalized autocorrelation function does not depend on T and n provided the parameter υ ≍ (n+1)τ/(2T) is used as an argument instead of time lag τ. When interpreting observed R(τ) one has to consider that as a consequence of a trend removal this function acquires characteristic wave-like form not obligatory caused by physics of the process. Time parameters of R(τ) oscillations are proportional to T/(n+1). Functions R(τ) and G(f) for the first order autoregression model are analysed. Comparison is given with formulas of other authors and with observational data.

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