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Title: Weighted CUSUM tests for the stability of the correlation structure of multivariate volatility models Authors:  Marco Barassi - University of Birmingham (United Kingdom) [presenting]
Brendan McCabe - University of Liverpool (United Kingdom)
Yuqian Zhao - University of Birmingham (United Kingdom)
Abstract: A weighted approximation of semi-parametric CUSUM statistics is proposed for the stability of correlation structures of multivariate volatility models. These weighted CUSUM tests are constructed so as to enhance their power in either ends of a sample. Since for CUSUM-type change-point tests the usual Sup-statistics are calculated over a trimmed sample, this renders impossible to detect change points in the trimmed proportion of the sample as well as in the vicinity of it. As such, these tests tend to lose the power when breaks occur close to either ends of the sample ($T-t^*\rightarrow \infty$ and $t^*\rightarrow \infty$, $T$ is the sample size and $1\leq t^*\leq \infty$ is the break location). Our tests overcome this type of issues using two types of weight functions, namely $q_1(u, \alpha)=(u\cdot (1-u))^\alpha, \quad 0\leq u \leq 1 $ and $q_2(u, \alpha)=(u\cdot(1-u)\cdot \log \log\frac{1}{u\cdot(1-u)})^\alpha, \quad 0\leq u \leq 1$, where $0 < \alpha < 1/2$ is a self-selected parameter. We derive the limiting distribution of the proposed tests under the null and assess their performance by means of Monte Carlo methods. The results obtained suggest that weighted CUSUM tests with weight function $[u\cdot(1-u)]^{\alpha}$ ($0<\alpha<1/2$) exhibit better performance. As an application, we use both standard semi-parametric CUSUM and weighted CUSUM tests to detect harmful events in the U.S. equity market in the years 2014, 2015 and 2016.