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

TL;DR

This paper extends a multiple filter test to detect variance changes in renewal processes, accounting for rate change points, with applications to neuronal spike train analysis.

Contribution

It introduces an adaptation of the MFT for variance homogeneity that incorporates rate change estimates, enabling detection of variance changes amidst rate shifts.

Findings

The extended MFT effectively detects variance change points.

The method remains robust despite small deviations from the Gaussian limit.

Application to neuronal data reveals diverse rate and variance change profiles.

Abstract

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