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Non-stationarity of the rate or variance of events is a well-known problem inthe description and analysis of time series of events, such as neuronal spiketrains. A multiple filter test (MFT) for rate homogeneity has been proposedearlier that detects change points on multiple time scales simultaneously. Itis based on a filtered derivative approach, and the rejection threshold derivesfrom a Gaussian limit process $L$ which is independent of the point processparameters.  Here we extend the MFT to variance homogeneity of life times. When the rateis constant, the MFT extends directly to the null hypothesis of constantvariance. In the presence of rate change points, we propose to incorporateestimates of these in the test for variance homogeneity, using an adaptation ofthe test statistic. The resulting limit process shows slight deviations from$L$ that depend on unknown process parameters. However, these deviations aresmall and do not considerably change the properties of the statistical test.This allows practical application, e.g.~to neuronal spike trains, whichindicates various profiles of rate and variance change points.

Multi-scale detection of variance changes in renewal processes in the presence of rate change points