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

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Author Info
Chor-yiu SIN
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)

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Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 476.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:476

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Keywords: Asymmetric distribution Cointegration LABF models multivariate GARCH price discovery WLS

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies

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  1. Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," CIRJE F-Series CIRJE-F-207, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  2. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 473-95, August. [Downloadable!] (restricted)
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  3. Engle, Robert F. & Patton, Andrew J., 2004. "Impacts of trades in an error-correction model of quote prices," Journal of Financial Markets, Elsevier, vol. 7(1), pages 1-25, January. [Downloadable!] (restricted)
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  4. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July. [Downloadable!] (restricted)
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  5. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  6. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-62, July.
  7. Franses, P.H. & Kofman, P. & Moser, J., 1992. "Garch Effects on a Test of Cointegration," Papers 9249-a, Erasmus University of Rotterdam - Econometric Institute.
  8. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, January. [Downloadable!]
  9. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February. [Downloadable!]
  10. Alexakis, Panayotis & Apergis, Nicholas, 1996. "ARCH effects and cointegration: Is the foreign exchange market efficient?," Journal of Banking & Finance, Elsevier, vol. 20(4), pages 687-697, May. [Downloadable!] (restricted)
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