IDEAS home Printed from https://ideas.repec.org/p/ecm/nasm04/476.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://repec.org/esNASM04/up.11078.1075550549.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    3. Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 Australasian Meetings 92, Econometric Society.
    4. 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," Econometric Reviews, Taylor & Francis Journals, vol. 22(2), pages 179-202.
    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.
    6. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    7. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    8. Kroner, Kenneth F. & Sultan, Jahangir, 1993. "Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(4), pages 535-551, December.
    9. 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.
    10. 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, vol. 48(5), pages 1779-1801, December.
    11. Joel Hasbrouck, 2003. "Intraday Price Formation in U.S. Equity Index Markets," Journal of Finance, American Finance Association, vol. 58(6), pages 2375-2400, December.
    12. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    13. Hasbrouck, Joel, 1995. "One Security, Many Markets: Determining the Contributions to Price Discovery," Journal of Finance, American Finance Association, vol. 50(4), pages 1175-1199, September.
    14. 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.
    15. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 Australasian Meetings 92, Econometric Society.
    2. White, Halbert & Pettenuzzo, Davide, 2014. "Granger causality, exogeneity, cointegration, and economic policy analysis," Journal of Econometrics, Elsevier, vol. 178(P2), pages 316-330.
    3. Blake LeBaron, 2013. "Heterogeneous Agents and Long Horizon Features of Asset Prices," Working Papers 63, Brandeis University, Department of Economics and International Business School, revised Sep 2013.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chor-yiu SIN, 2004. "Estimation and Testing for Partially Nonstationary Vector Autoregressive Models with GARCH: WLS versus QMLE," Econometric Society 2004 Australasian Meetings 92, Econometric Society.
    2. López Cabrera, Brenda & Schulz, Franziska, 2016. "Volatility linkages between energy and agricultural commodity prices," Energy Economics, Elsevier, vol. 54(C), pages 190-203.
    3. Suhejla Hoti & Felix Chan & Michael McAleer, 2003. "Structure and Asymptotic Theory for Multivariate Asymmetric Volatility: Empirical Evidence for Country Risk Ratings," CIRJE F-Series CIRJE-F-203, CIRJE, Faculty of Economics, University of Tokyo.
    4. Massimiliano Caporin & Michael McAleer, 2011. "Thresholds, news impact surfaces and dynamic asymmetric multivariate GARCH," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(2), pages 125-163, May.
    5. Hakim, Abdul & McAleer, Michael, 2009. "Forecasting conditional correlations in stock, bond and foreign exchange markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2830-2846.
    6. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, January.
    7. Lanza, Alessandro & Manera, Matteo & McAleer, Michael, 2006. "Modeling dynamic conditional correlations in WTI oil forward and futures returns," Finance Research Letters, Elsevier, vol. 3(2), pages 114-132, June.
    8. Silvennoinen, Annastiina & Teräsvirta, Timo, 2024. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," Econometrics and Statistics, Elsevier, vol. 32(C), pages 57-72.
    9. Yudong Wang & Chongfeng Wu & Li Yang, 2015. "Hedging with Futures: Does Anything Beat the Naïve Hedging Strategy?," Management Science, INFORMS, vol. 61(12), pages 2870-2889, December.
    10. Neifar, Malika, 2020. "Multivariate GARCH Approaches: case of major sectorial Tunisian stock markets," MPRA Paper 99658, University Library of Munich, Germany.
    11. Vicente Meneu & Hipòlit Torró, 2003. "Asymmetric covariance in spot‐futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(11), pages 1019-1046, November.
    12. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    13. Abdul Hakim & Michael McAleer, 2009. "VaR Forecasts and Dynamic Conditional Correlations for Spot and Futures Returns on Stocks and Bonds," CIRJE F-Series CIRJE-F-676, CIRJE, Faculty of Economics, University of Tokyo.
    14. Martínez, Beatriz & Torró, Hipòlit, 2015. "European natural gas seasonal effects on futures hedging," Energy Economics, Elsevier, vol. 50(C), pages 154-168.
    15. Kin-Yip Ho & Albert K Tsui, 2008. "Volatility Dynamics in Foreign Exchange Rates : Further Evidence from the Malaysian Ringgit and Singapore Dollar," Finance Working Papers 22571, East Asian Bureau of Economic Research.
    16. Dahiru A. Balaa & Taro Takimotob, 2017. "Stock markets volatility spillovers during financial crises: A DCC-MGARCH with skewed-t density approach," Borsa Istanbul Review, Research and Business Development Department, Borsa Istanbul, vol. 17(1), pages 25-48, March.
    17. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    18. Annastiina Silvennoinen & Timo Ter�svirta, 2015. "Modeling Conditional Correlations of Asset Returns: A Smooth Transition Approach," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 174-197, February.
    19. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    20. Li, Ming-Yuan Leon, 2008. "Clarifying the dynamics of the relationship between option and stock markets using the threshold vector error correction model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 511-520.

    More about this item

    Keywords

    Asymmetric distribution; Cointegration; LABF models; multivariate GARCH; price discovery; WLS;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:nasm04:476. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.