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A general statistical test for correlations in a finite-length time series

A general statistical test for correlations in a finite-length time series

Journal of Chemical Physics 128(21): 214101

The statistical properties of the autocorrelation function from a time series composed of independently and identically distributed stochastic variables has been studied. Analytical expressions for the autocorrelation function's variance have been derived. It has been found that two common ways of calculating the autocorrelation, moving-average and Fourier transform, exhibit different uncertainty characteristics. For periodic time series, the Fourier transform method is preferred because it gives smaller uncertainties that are uniform through all time lags. Based on these analytical results, a statistically robust method has been proposed to test the existence of correlations in a time series. The statistical test is verified by computer simulations and an application to single-molecule fluorescence spectroscopy is discussed.

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Accession: 051139179

Download citation: RISBibTeXText

PMID: 18537409

DOI: 10.1063/1.2931943

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