On Testing for a Change-Point in Variance of Normal Distribution

Abstract

This paper addresses the problem of testing for a change about the variance of sequence of normal random variables with unknown means. It compares the power performance of five tests, namely: L-test based on Lehmann's (1951) U-statistic, B-test based on bayesian method, R-test derived from likelihood method, C-test based on Brown et al.'s (1975) CUSUM of squares method and finally, the LM-test based on Nyblom's (1989) and Hansen's (1991) Lagrange multiplier method. An empirical power comparison of the five tests suggests that none of the tests power lead to another. However, it is observed that when change-point is between the beginning and the mid portion, the L and R test are better and when the change-point is between the mid portion and the end, CUSUM of square and the B test are better as compared to the other tests.

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