A New Bootstrap Test for Multiple Assets Joint Risk Testing

Abstract

In this paper, a novel simulation-based methodology is proposed to test the validity of a set of marginal time series models, where the dependence structure between the time series is taken directly from the observed data. The procedure is useful when one wants to summarize the test results for several time series in one joint test statistic and p value. The proposed test method can have higher statistical power than a test for a univariate time series, especially for short time series. Therefore, our test for multiple time series is particularly useful if one wants to assess value-at-risk (or expected shortfall) predictions within a small time frame (eg, a crisis period). We apply our method to test generalized autoregressive conditional heteroscedasticity (GARCH) model specifications for a large panel data set of stock returns.

Keywords: bootstrap test, generalized autoregressive conditional heteroscedasticity (GARCH), marginal models, multiple time series, value-at-risk (VaR)