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

Jeffery A. Hanson, Haw Yang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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.

Original languageEnglish (US)
Article number214101
JournalJournal of Chemical Physics
Issue number21
StatePublished - 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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