Items ordered in time usually are not independent of one another; thus, some modifications must be made in the usual regression or harmonic analysis of such data;The number of independent events in such a time series can be approximated by dividing the total number of observations by the number of the first lag which will produce a non-significant serial correlation coefficient;The distributions and significance levels of the serial covariance have been indicated;If the series consists of a large number of items, the large sample normal distribution of the serial R can be used;For small samples, we have calculated what we purport to call the general density and probability functions for N odd and lag 1. The 1% and 5% significance levels for N up to 45 have been tabulated;It has been indicated that the same distributions hold for RL as for Ri when N is a prime number or when L and N have no common factor. Some of the distributions of RL for L a factor of N have been derived and directions presented for extensions;Several examples of the calculations of the serial correlation coefficients have been set up, illustrating applications to Wold's analysis of time series and to the problem of estimating the amount of information contained in various series;Points to be considered in the future are: discussion of type II error, extension to other fields than that of economic time series, a more vigorous test of the significance of the regression and harmonic coefficients in a serially correlated series, an extension of the distributions to include more lags of higher order than those considered in this manuscript and, above all, distributions and significance levels of RL when the data are corrected for trend effects.