(A) modified CUSUM (MCUSUM) algorithm for gradual change detection in a time series data

Abstract

The main objective in a change point detection problem is to develop algorithms for efficient detection of gradual and /or abrupt changes in the parameter distribution of a time series data. In this dissertation, we propose a Modified Cumulative Sum (MCUSUM) algorithm for the detection of the start and end time points of a gradual change in the mean value of a time series data based on the Likelihood Ratio and Maximum Likelihood principles. The design, implementation and performance of the proposed algorithm for a gradual change detection is evaluated and compared to the existing algorithms used for the detection of abrupt and /or gradual change in the process mean known as the CUSUM and Chen and Gupta (C&G) algorithms respectively, using the mean detection delay as the performance measure. The performance of the three algorithms is evaluated using Monte Carlo Simulations. In terms of the mean detection delay, the MCUSUM procedure is found to have a comparably good performance than the two existing algorithms for the detection of the two change points.