A note on the use of serial measures in spike train analysis and their relation to the corresponding moments

A spike train is a sequence of interspike intervals and should be described in terms of random variables. So, in order to recognize the information of the spike train, one usually calculates the sample mean (as the normalized sum of all intervals in one realization) or the means (of outcomes of respective intervals), an approximation of which is the PSTH. Further, the sample variance and variance, the serial correlation, and the autocovariance are utilized for evaluation. In this paper it is shown that these notions, which seem to be very similar, have little to do one with another, except for some cases (stationarity, ergodicity), which rarely occur in neurobiology. Finally, it is proposed to rename the term stationarity in spike train analysis, because it differs considerably from the definition which is used in the theory of random variables and stochastic processes.