A self-normalization break test for correlation matrix

We construct a new test for correlation matrix break based on the self-normalization method. The self-normalization test has practical advantage over the existing test: easy and stable implementation; not having the singularity issue and the bandwidth selection issue of the existing test; remedying size distortion problem of the existing test under (near) singularity, serial dependence, conditional heteroscedasticity or unconditional heteroscedasticity. This advantage is demonstrated experimentally by a Monte-Carlo simulation and theoretically by showing no need for estimation of complicated covariance matrix of the sample correlations. We establish the asymptotic null distribution and consistency of the self-normalization test. We apply the correlation matrix break tests to the stock log returns of the companies of 10 largest weight of the NASDAQ 100 index and to five volatility indexes for options on individual equities.