Physics
Scientific paper
Dec 1964
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1964jatp...26.1239a&link_type=abstract
Journal of Atmospheric and Terrestrial Physics, vol. 26, no. 12, pp. 1239-1255
Physics
3
Scientific paper
An investigation is made of the errors in correlation between pairs of autocorrelated series. The expressions usually given for the standard deviation of correlation coefficients of samples drawn from a population are for series in which the individual members are independent of one another. Using time series which were constructed to have a known autocorrelation function, p([rho]), it is found that the expression for the standard deviation of correlation coefficients for the non-autocorrelated series is also valid for the autocorrelated series if a "reduced" size is substituted for the size of the sample in the expression. The "reduction factor" is found to be equal to [is proportional to][infinity]-[infinity] [rho]2([tau]) d[tau]. Correlation functions of samples of time series are found to be normally oscillatory when they should take values close to zero and hence, smooth oscillations of sample correlation functions could be entirely spurious. The presence of such oscillations should not be taken to imply, necessarily, that the true correlation function is oscillatory.
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