  The statistical analysis of neuronal spike trains by models of point
processes often relies on the assumption of constant process parameters.
However, it is a well-known problem that the parameters of empirical spike
trains can be highly variable, such as for example the firing rate. In order to
test the null hypothesis of a constant rate and to estimate the change points,
a Multiple Filter Test (MFT) and a corresponding algorithm (MFA) have been
proposed that can be applied under the assumption of independent inter spike
intervals (ISIs).
  As empirical spike trains often show weak dependencies in the correlation
structure of ISIs, we extend the MFT here to point processes associated with
short range dependencies. By specifically estimating serial dependencies in the
test statistic, we show that the new MFT can be applied to a variety of
empirical firing patterns, including positive and negative serial correlations
as well as tonic and bursty firing. The new MFT is applied to a data set of
empirical spike trains with serial correlations, and simulations show improved
performance against methods that assume independence. In case of positive
correlations, our new MFT is necessary to reduce the number of false positives,
which can be highly enhanced when falsely assuming independence. For the
frequent case of negative correlations, the new MFT shows an improved detection
probability of change points and thus, also a higher potential of signal
extraction from noisy spike trains.
