Tests for Variance Shift at an Unknown Time Point

Abstract

SUMMARY Two tests for variance shift in a sequence of independent normal random variables, when the initial level of variance is unknown, are investigated in this article. The first is a locally most powerful test, and the second is a test based upon cusums of x2 values. Distribution functions of the two test statistics are approximated through the use of Edgeworth expansions and/or the beta distribution by matching the first few moments. Critical points of both test statistics are tabulated for various sample sizes. Powers of the two tests are compared using a Monte Carlo example. An illustration of the application of the tests to stock market price analysis is provided.