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Multi‐Scale Detection of Variance Changes in Renewal Processes in the Presence of Rate Change Points
Author(s) -
Albert Stefan,
Messer Michael,
Schiemann Julia,
Roeper Jochen,
Schneider Gaby
Publication year - 2017
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12254
Subject(s) - mathematics , homogeneity (statistics) , statistics , variance (accounting) , statistic , point process , statistical hypothesis testing , gaussian , gaussian process , physics , accounting , quantum mechanics , business
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, for example, to neuronal spike trains, which indicates various profiles of rate and variance change points.