Some remarks on the calculation of the serial correlation coefficient in the analysis of time series

In the analysis of time series the autocorrelation or serial correlation coefficient is calculated in a manner not quite analogous to the ordinary correlation coefficient. The difference between these two versions is investigated, mainly in the spirit of descriptive statistics. It emerges, that the version of time series analysis tends to be smaller in absolute value than the ordinary coefficient. For confirmation of this result a threefold approach is taken: In section 3 it is shown, that it holds asymptotically for a large number N of observations. In section 4 three simple models of time series are considered, which show the predicted behaviour of the two versions of the autocorrelation coefficient. In section 5 a numerical example is given. Here one can see, that exceptions from the general rule are possible. Therefore emphasis on the asymptotic behaviour is crucial. To consider the problem from a stochastic viewpoint, i.e. the investigation of the sampling behaviour of the two versions seems much more difficult. Therefore in the last section only some results concerning the autocovariance coefficient are derived, which show, that in this case there is no gain in unbiasedness, if the traditional form of the coefficient is used.