Robust Score and Portmanteau Tests of Volatility Spillover

This paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or GARCH-type feedback. The tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent. We negligibly trim test equations, or components of the equations, and construct heavy tail robust score and portmanteau statistics. Trimming is either simple based on an indicator function, or smoothed. In particular, we develop the tail-trimmed sample correlation coefficient for robust inference, and prove that its Gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness. Further, if spillover occurs within a specified horizon, our test statistics obtain power of one asymptotically. We discuss the choice of trimming portion, including a smoothed p-value over a window of extreme observations. A Monte Carlo study shows our tests provide significant improvements over extant GARCH-based tests of spillover, and we apply the tests to financial returns data. Finally, based on ideas in Patton (2011) we construct a heavy tail robust forecast improvement statistic, which allows us to demonstrate that our spillover test can be used as a model specification pre-test to improve volatility forecasting.