An empirical study of the impact of data dimensionality on the performance of change point detection algorithms

Abstract: When a system is monitored over time, changes can be discovered in the time series of monitored variables. Change Point Detection (CPD) aims at finding the time point where a change occurs in the monitored system. While CPD methods date back to the 1950’s with applications in quality control, few studies have been conducted on the impact of data dimensionality on CPD algorithms. This thesis intends to address this gap by examining five different algorithms using synthetic data that incorporates changes in mean, covariance, and frequency across dimensionalities up to 100. Additionally, the algorithms are evaluated on a collection of data sets originating from various domains. The studied methods are then assessed and ranked based on their performance on both synthetic and real data sets, to aid future users in selecting an appropriate CPD method. Finally, stock data from the 30 most traded companies on the Swedish stock market are collected to create a new CPD data set to which the CPD algorithms are applied. The changes of the monitored system that the CPD algorithms aim to detect are the changes in policy rate set by the Swedish central bank, Riksbank. The results of the thesis show that the dimensionality impacts the accuracy of the methods when noise is present and when the degree of mean or covariance change is small. Additionally, the application of the algorithms on real world data sets reveals large differences in performance between the studied methods, underlining the importance of comparison studies. Ultimately, the kernel based CPD method performed the best across the real world data set employed in the thesis.