Abstract: Risk transmission among financial markets and their participants is time-evolving, especially for extreme risk scenarios. Possibly sudden time variation of such risk structures asks for quantitative techniques that can cope with such situations. Here we present a novel localized multivariate CAViaR-type model to respond to the challenge of time-varying risk contagion. For this purpose, we construct a test for parameter homogeneity with totally data-driven critical values. We prove that these critical values lead to the required confidence level. Based on this test, we propose an estimation procedure that adapts to a possible time-variation of the parameter. A comprehensive simulation study supports the effectiveness of our approach in detecting structural changes in multivariate CAViaR. Finally, when applying for the US and German financial markets, we can trace out the dynamic tail risk spillovers and find that the US market appears to play a dominant role in risk transmissions, especially in volatile market periods.

Key words and phrases: Change point detection, conditional quantile autoregression, local parametric approach, multiplier bootstrap.