Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE

Abstract

Macroeconomic or financial data are often modelled with cointegration and GARCH. Noticeable examples include those studies of price discovery, in which stock prices of the same underlying asset are cointegrated and they exhibit multivariate GARCH. Modifying the asymptotic theories developed in Li, Ling and Wong (2001) and Sin and Ling (2004), this paper proposes a WLS(weighted least squares) for the parameters of an ECM(error-correction model). Apart from its computational simplicity, by construction, the consistency of WLS is insensitive to possible misspecification in conditional variance. Further, asymmetrically distributed deflated error is allowed, at the expense of more involved asymptotic distributions of the statistics. Efficiency loss relative to QMLE(quasi-maximum likelihood estimator) is discussed within the class of LABF(locally asymptotically Brownian functional) models. The insensitivity and efficiency of WLS in finite samples are examined through Monte Carlo experiments. We also apply the WLS to an empirical example of HSI(Hang Seng Index), HSIF(Hang Seng Index Futures) and TraHK(Hong Kong Tracker Fund).Asymmetric distribution; Cointegration; LABF models; Multivariate GARCH; Price discovery; WLS