The MOSUM of squares test for monitoring variance changes

In this paper we propose the MOSUM of squares test for monitoring potential variance changes when new observations arrive. It is shown that the limiting distribution of the proposed test is determined by the increments of the Brownian bridge. Finite-sample simulations examine empirical sizes and average detection delays of the proposed test. We apply the proposed test to study how soon a variance change can be detected for the yen/$ exchange rate and the S&P 500 stock index.