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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

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)

Suggested Citation

  • Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 North American Summer Meetings 476, Econometric Society.
  • Handle: RePEc:ecm:nasm04:476
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    References listed on IDEAS

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    1. 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.
    2. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
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    5. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
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    11. 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 351-362, 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, vol. 178(P2), pages 316-330.

    More about this item

    Keywords

    Asymmetric distribution; Cointegration; LABF models; multivariate GARCH; price discovery; WLS;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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