IDEAS home Printed from https://ideas.repec.org/p/ecm/ausm04/92.html

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 Australasian Meetings 92, Econometric Society.
    • Handle: RePEc:ecm:ausm04:92
    as

    Download full text from publisher

    File URL: http://repec.org/esAUSM04/up.19704.1076993265.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert Engle & Clive Granger, 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    8. 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, The University of Osaka.
    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. 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.
    12. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(4), pages 541-564, August.
    13. Anders Rahbek & Rocco Mosconi, 1999. "Cointegration rank inference with stationary regressors in VAR models," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 76-91.
    14. Shiqing Ling & W. K. Li, 1997. "Diagnostic checking of nonlinear multivariate time series with multivariate arch errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 447-464, September.
    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 North American Summer Meetings 476, Econometric Society.
    2. 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.
    3. White, Halbert & Pettenuzzo, Davide, 2014. "Granger causality, exogeneity, cointegration, and economic policy analysis," Journal of Econometrics, Elsevier, vol. 178(P2), pages 316-330.

    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 North American Summer Meetings 476, Econometric Society.
    2. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, August.
    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. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, The University of Osaka.
    5. Sugra Humbatova & Afag Huseyn & Natig Gadim-Oglu Hajiyev, 2023. "Impact of Oil Factor on Investment: The Case of Azerbaijan," International Journal of Energy Economics and Policy, Econjournals, vol. 13(2), pages 129-148, March.
    6. 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.
    7. G. Everaert, 2007. "Estimating Long-Run Relationships between Observed Integrated Variables by Unobserved Component Methods," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/452, Ghent University, Faculty of Economics and Business Administration.
    8. 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.
    9. Kuo, Biing-Shen, 1998. "Test for partial parameter instability in regressions with I(1) processes," Journal of Econometrics, Elsevier, vol. 86(2), pages 337-368, June.
    10. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    11. Peña, Daniel & Poncela, Pilar, 1997. "Eigenstructure of nonstationary factor models," DES - Working Papers. Statistics and Econometrics. WS 6224, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Martínez, Beatriz & Torró, Hipòlit, 2015. "European natural gas seasonal effects on futures hedging," Energy Economics, Elsevier, vol. 50(C), pages 154-168.
    13. López Cabrera, Brenda & Schulz, Franziska, 2016. "Volatility linkages between energy and agricultural commodity prices," Energy Economics, Elsevier, vol. 54(C), pages 190-203.
    14. 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.
    15. Khalfaoui, R & Boutahar, M, 2012. "Portfolio risk evaluation: An approach based on dynamic conditional correlations models and wavelet multiresolution analysis," MPRA Paper 41624, University Library of Munich, Germany.
    16. Pesaran, M. Hashem & Shin, Yongcheol & Smith, Richard J., 2000. "Structural analysis of vector error correction models with exogenous I(1) variables," Journal of Econometrics, Elsevier, vol. 97(2), pages 293-343, August.
    17. Billio, Monica & Caporin, Massimiliano, 2009. "A generalized Dynamic Conditional Correlation model for portfolio risk evaluation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2566-2578.
    18. Neifar, Malika, 2020. "Multivariate GARCH Approaches: case of major sectorial Tunisian stock markets," MPRA Paper 99658, University Library of Munich, Germany.
    19. Stelios D. Bekiros, 2013. "Decoupling and the Spillover Effects of the US Financial Crisis: Evidence from the BRIC Markets," Working Paper series 21_13, Rimini Centre for Economic Analysis.
    20. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Multivariate GARCH Models," Springer Books, in: Thomas Mikosch & Jens-Peter Kreiß & Richard A. Davis & Torben Gustav Andersen (ed.), Handbook of Financial Time Series, chapter 9, pages 201-229, Springer.

    More about this item

    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:ausm04:92. 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.