Performance comparison of two segmentation algorithms using growing reference windows

Abstract

Two procedures designed for the detection of parameter jumps in autoregressive gaussian distributed processes — the generalized likelihood ratio (GLR) algorithm and the cumulated sum (CUSUM) algorithm — are compared regarding their performance. Both algorithms share as a common feature a growing reference window and a sliding fixed length test window, but use different detection statistics. Some rough features of the algorithms are deducted using means instead of the stochastic signal itself. More detailed results are then obtained from extensive simulations performed with different types of parameter jumps in the test signals. As a general result, it is shown that the CUSUM procedure may perform slightly better with respect to the detection of spurious jumps, if direction and distance of the jump is known in advance. On the other hand, the GLR algorithm leads to much better results in the detection and particularly the positioning of jumps succeeding each other in a short time interval (“short segments”). Moreover, the GLR algorithm is more robust considering the application of a segmentation procedure under realistic assumptions.