A break test for the tail-event correlation matrix based on the self-normalization method

Break tests for tail event correlation matrix based on the self-normalization method are proposed in which quantiles are admitted to be time varying and are nonparametrically estimated by a kernel method. The proposed test is simply modified to test for break of cross-quantilogram of Han et al. (J Econ 193: 251–270, 2016), which is a measure of predictability of one tail event by lags of another tail event. We construct the limiting null distributions of the proposed break tests. Monte Carlo experiment reveals that the oversize problems of the existing break test by Hoga (Biometrika 105:627–643, 2018) for bivariate samples with conditional heteroscedasticity and for the samples with mean change and/or variance changes are resolved by the proposed break test. The experiment also shows finite sample validity of the proposed break tests for the tail event correlation matrix of multivariate random variables. The break tests are applied for illustrations of breaks in tail event correlations and predictability of log returns of the US and an European stock price indices.