A Portmanteau Test for Multivariate GARCH when the Conditional Mean is an ECM: Theory and Empirical Applications

Abstract

Macroeconomic or financial data are often modelled with cointegration and GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity). Noticeable examples include those studies of price discovery in which stock prices of the same underlying asset are cointegrated and they exhibit multivariate GARCH. It was not until recently that Li, Ling, and Wong's (2001) Biometrika, 88, 1135–1152, paper formally derived the asymptotic distribution of the estimators for the error-correction model (ECM) parameters, in the presence of conditional heteroskedasticity. As far as ECM parameters are concerned, the efficiency gain may be huge even when the deflated error is symmetrically distributed. Taking into consideration the different rates of convergence, this paper first shows that the standard distribution applies to a portmanteau test, even when the conditional mean is an ECM. Assuming the usual null of no multivariate GARCH, the performance of this test in finite samples is examined through Monte Carlo experiments. We then apply the test for GARCH to the yearly or quarterly (extended) Nelson–Plosser data, embedded with some prototype multivariate models. We also apply the test to the intra-daily HSI (Hang Seng Index) and its derivatives, with the spread as the ECT (error-correction term). The empirical results throw doubt on the efficiency of the usual estimation of the ECM parameters, and more importantly, on the validity of the significance tests of an ECM.