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

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  • Chor-yiu SIN
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    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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    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 92.

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    Date of creation: 11 Aug 2004
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    Handle: RePEc:ecm:ausm04:92

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    Keywords: Asymmetric distribution; Cointegration; LABF models; Multivariate GARCH; Price discovery; WLS;

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    1. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper, Institute of Social and Economic Research, Osaka University 0548, Institute of Social and Economic Research, Osaka University.
    2. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, Econometric Society, vol. 61(4), pages 783-820, July.
    3. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 280-310, April.
    4. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 251-76, March.
    5. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 53(4), pages 473-95, August.
    6. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, American Finance Association, vol. 48(5), pages 1779-1801, December.
    7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 12(2-3), pages 231-254.
    8. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(04), pages 541-564, August.
    9. Anders Rahbek & Rocco Mosconi, 1999. "Cointegration rank inference with stationary regressors in VAR models," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 2(1), pages 76-91.
    10. 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, American Statistical Association, vol. 20(3), pages 351-62, July.
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    Cited by:
    1. White, Halbert & Pettenuzzo, Davide, 2014. "Granger causality, exogeneity, cointegration, and economic policy analysis," Journal of Econometrics, Elsevier, Elsevier, vol. 178(P2), pages 316-330.

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