“Distributions of Correlation Coefficients in Economic Time Series”, 1961 (; backlinks; similar):
This paper presents results, mainly in tabular form, of a sampling experiment in which 100 economic time series 25 years long were drawn at random from the Historical Statistics for the United States. Sampling distributions of coefficients of correlation and autocorrelation were computed using these series, and their logarithms, with and without correction for linear trend.
We find that the frequency distribution of autocorrelation coefficients has the following properties:
It is roughly invariant under logarithmic transformation of data.
It is approximated by a Pearson Type XII function.
It approaches a rectangular distribution symmetric about 0 as the lag increases.
The autocorrelation properties observed are not to be explained by linear trends alone. Correlations and lagged cross-correlations are quite high for all classes of data. eg. given a randomly selected series, it is possible to find, by random drawing, another series which explains at least 50% of the variances of the first one, in 2–6 random trials, depending on the class of data involved. The sampling distributions obtained provide a basis for tests of statistical-significance of correlations of economic time series. We also find that our economic series are well described by exact linear difference equations of low order.