Change Point Detection of Periodic Data
Open AccessThe purpose of this dissertation is to construct change point detection methods for periodic data in both offline and online settings. We first propose three methods to test the equality of two matrix distributions: the likelihood ratio test, the Frobenius norm methods and triangle tests. We present a simulation to compare their performance under the matrix normal distributions. We apply the testing methods to compare the US economy, as measured by closing prices of five market indices, before and after the US stock market crash of 2008.We consider offline detection of multiple changes in the distribution of periodic and autocorrelated data with known period. We propose methods of testing the equality of matrix distributions and present methods that can be applied to matrix observations using the E-divisive algorithm. We show that periodicity and autocorrelation degrade existing change detection methods because they blur the changes that these procedures aim to discover. Methods that ignore the periodicity have low power to detect changes in the mean and the variance of periodic data when the periodic effects overwhelm the true changes, while the proposed methods detect such changes with high power.Online change point detection methods monitor changes in the distribution of a data stream. Based on the sliding-window and depth function models, we present two nonparametric online change detection methods that are applicable to observations in
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