+ Site Statistics

+ Search Articles

+ PDF Full Text Service

How our service works

Request PDF Full Text

+ Follow Us

Follow on Facebook

Follow on Twitter

Follow on LinkedIn

+ Subscribe to Site Feeds

Most Shared

PDF Full Text

+ Translate

+ Recently Requested

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

Hanson, J.A.; Yang, H.

Journal of Chemical Physics 128(21): 214101

2008

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.

Related references

**Statistical test of the hypothesis that a time series is stationary**. Geophysics 32(3): 499-511, 1967