  Nonstationarity of the event rate is a persistent problem in modeling time
series of events, such as neuronal spike trains. Motivated by a variety of
patterns in neurophysiological spike train recordings, we define a general
class of renewal processes. This class is used to test the null hypothesis of
stationary rate versus a wide alternative of renewal processes with finitely
many rate changes (change points). Our test extends ideas from the filtered
derivative approach by using multiple moving windows simultaneously. To adjust
the rejection threshold of the test, we use a Gaussian process, which emerges
as the limit of the filtered derivative process. We also develop a multiple
filter algorithm, which can be used when the null hypothesis is rejected in
order to estimate the number and location of change points. We analyze the
benefits of multiple filtering and its increased detection probability as
compared to a single window approach. Application to spike trains recorded from
dopamine midbrain neurons in anesthetized mice illustrates the relevance of the
proposed techniques as preprocessing steps for methods that assume rate
stationarity. In over 70% of all analyzed spike trains classified as rate
nonstationary, different change points were detected by different window sizes.
