A Method to Estimate the Statistical Significance of a Correlation When the Data Are Serially Correlated

When analyzing pairs of time series, one often needs to know whether a correlation is statistically significant. If the data are Gaussian distributed and not serially correlated, one can use the results of classical statistics to estimate the significance. While some techniques can handle non-Gaussian distributions, few methods are available for data with nonzero autocorrelation (i.e., serially correlated). In this paper, a nonparametric method is suggested to estimate the statistical significance of a computed correlation coefficient when serial correlation is a concern. This method compares favorably with conventional methods.