Investigating the Finite Sample Properties of Causality-in-Variance Tests: A MC Approach

In this paper we examine, through comprehensive Monte Carlo simulations, the finite sample performance of four causality-in-variance test procedures: Hong’s [Hong, Y., 2001. A test for volatility spillover with an application to exchange rates. Journal of Econometrics 103, 183-224] kernel based cross correlation Q test, Cheung and Ng’s [Cheung, Y.M., Ng, L.K., 1996. A causality-in-variance test and its application to financial market prices. Journal of Econometrics 72, 33-48] cross correlation S test, Comte and Lieberman’s [Comte, F., Lieberman, O., 2000. Second order noncausality in multivariate CARCH processes. Journal of Time Series Analysis 21, 535-557] Likelihood Ratio (LR) test, and Hafner and Herwartz’s [Hafner, C.M., Herwartz, H., 2006. A Langrange multiplier test for causality in variance. Economics Letters 93, 137-141] Langrange Multiplier (LM) test. Our results show that Comte and Lieberman’s LR as well as and Hafner and Herwartz’s LM tests suffer from severe size distortions, while they demonstrate very low power, under long horizon causality alternatives. Both cross correlation tests are reasonably well sized. However, Hong’s Q test demonstrates less sensitivity to arbitrary choices of the weighting scheme and alternative volatility dynamics, when compared to Cheung and Ng’s S test.  Furthermore, cross correlations tests are favorably compared to LR and LM tests in terms of empirical power under a sequence of local alternatives. Our results reveal that the power performances of Q and S tests greatly depend on the choice of bandwidth and lag truncation respectively. Motivated by these findings, we introduce a simple method for automatic bandwidth selection used in Hong’s Q test calculations. The simulation results show that the implementation of our procedure ensures high finite sample power. An empirical application to macroeconomic and financial data is also provided.