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The amount of information given by a statistical estimate is defined as the reciprocal of the variance of the estimate. In this study, a random series is adopted as the standard of information content. The relative information content of the mean for various types of hydrologic series is defined as the ratio of the variance of the mean for a random series to the variance of the mean for given types of series. Beyond the well-known fact that the sequential correlation in hydrologic series reduces the effective length of the series, the sequential correlation tends to impair the effectiveness of cross-correlations between series. There are limits, therefore, upon increasing the information content of a mean by utilizing the information contained in a related series. Moreover, cross-correlation tends to decrease the effective length of series for computing regional means.
Matalas et al. (1962) studied this question.