IDEAS home Printed from https://ideas.repec.org/p/eui/euiwps/eco2009-42.html
   My bibliography  Save this paper

Generalized Least Squares Estimation for Cointegration Parameters Under Conditional Heteroskedasticity

Author

Listed:
  • Helmut Herwartz
  • Helmut Luetkepohl

Abstract

In the presence of generalized conditional heteroscedasticity (GARCH) in the residuals of a vector error correction model (VECM), maximum likelihood (ML) estimation of the cointegration parameters has been shown to be efficient. On the other hand, full ML estimation of VECMs with GARCH residuals is computationally di±cult and may not be feasible for larger models. Moreover, ML estimation of VECMs with independently identically distributed residuals is known to have potentially poor small sample properties and this problem also persists when there are GARCH residuals. A further disadvantage of the ML estimator is its sensitivity to misspecification of the GARCH process. We propose a feasible generalized least squares estimator which addresses all these problems. It is easy to compute and has superior small sample properties in the presence of GARCH residuals.

Suggested Citation

  • Helmut Herwartz & Helmut Luetkepohl, 2009. "Generalized Least Squares Estimation for Cointegration Parameters Under Conditional Heteroskedasticity," Economics Working Papers ECO2009/42, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2009/42
    as

    Download full text from publisher

    File URL: http://cadmus.eui.eu/dspace/bitstream/1814/12965/1/ECO_2009_42.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January.
    3. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    4. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(1), pages 1-27, March.
    5. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    6. 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.
    7. Seo, Byeongseon, 2007. "Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 137(1), pages 68-111, March.
    8. Christian M. Hafner & Helmut Herwartz, 2009. "Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(3), pages 294-323, August.
    9. 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.
    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. Westerlund, Joakim, 2014. "On the choice of test for a unit root when the errors are conditionally heteroskedastic," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 40-53.
    2. Anna Pajor & Justyna Wróblewska, 2022. "Forecasting performance of Bayesian VEC-MSF models for financial data in the presence of long-run relationships," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 427-448, September.
    3. Joakim Westerlund & Paresh Narayan, 2013. "Testing the Efficient Market Hypothesis in Conditionally Heteroskedastic Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(11), pages 1024-1045, November.
    4. Joakim Westerlund, 2013. "A computationally convenient unit root test with covariates, conditional heteroskedasticity and efficient detrending," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 477-495, July.
    5. Li, Y-N. & Chen, J. & Linton, O., 2021. "Estimation of Common Factors for Microstructure Noise and Efficient Price in a High-frequency Dual Factor Model," Cambridge Working Papers in Economics 2150, Faculty of Economics, University of Cambridge.
    6. López Cabrera, Brenda & Schulz, Franziska, 2016. "Volatility linkages between energy and agricultural commodity prices," Energy Economics, Elsevier, vol. 54(C), pages 190-203.

    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. de Goeij, Peter & Marquering, Wessel, 2009. "Stock and bond market interactions with level and asymmetry dynamics: An out-of-sample application," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 318-329, March.
    2. PRITI Verma, 2016. "The Impact Of Exchange Rates And Interest Rates On Bank Stock Returns: Evidence From U.S. Banks," Studies in Business and Economics, Lucian Blaga University of Sibiu, Faculty of Economic Sciences, vol. 11(1), pages 124-139, April.
    3. Anil K. Bera & Philip Garcia & Jae-Sun Roh, 1997. "Estimation of Time-Varying Hedge Ratios for Corn and Soybeans: BGARCH and Random Coefficient Approaches," Finance 9712007, University Library of Munich, Germany.
    4. Julien Chevallier, 2012. "Time-varying correlations in oil, gas and CO 2 prices: an application using BEKK, CCC and DCC-MGARCH models," Applied Economics, Taylor & Francis Journals, vol. 44(32), pages 4257-4274, November.
    5. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, January.
    6. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    7. Kamel Malik Bensafta, 2014. "A Regional Analysis of Markets Uncertainty Spillovers," Working Papers halshs-01015435, HAL.
    8. Warren Dean & Robert Faff, 2011. "Feedback trading and the behavioural ICAPM: multivariate evidence across international equity and bond markets," Applied Financial Economics, Taylor & Francis Journals, vol. 21(22), pages 1665-1678.
    9. Haigh, Michael S. & Bryant, Henry L., 2000. "Price And Price Risk Dynamics In Barge And Ocean Freight Markets And The Effects On Commodity Trading," 2000 Conference, April 17-18 2000, Chicago, Illinois 18934, NCR-134 Conference on Applied Commodity Price Analysis, Forecasting, and Market Risk Management.
    10. Olivier Massol & Albert Banal-Estañol, 2011. "Export diversification and resource-based industrialization : the case of natural gas," Working Papers hal-01031565, HAL.
    11. Michael S. Haigh & Henry L. Bryant, 2000. "The effect of barge and ocean freight price volatility in international grain markets," Agricultural Economics, International Association of Agricultural Economists, vol. 25(1), pages 41-58, June.
    12. Idier, J., 2006. "Stock exchanges industry consolidation and shock transmission," Working papers 159, Banque de France.
    13. Guillermo Benavides & Isela Elizabeth Téllez-León & Francisco Venegas-Martínez, 2015. "Effects of Volatility of the Exchange Rate on Inflation Expectations and Growth Prospects in Mexico (2002-2014)," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 63-78, November.
    14. Christodoulakis, George A., 2007. "Common volatility and correlation clustering in asset returns," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1263-1284, November.
    15. 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.
    16. Joakim Westerlund & Paresh Narayan, 2013. "Testing the Efficient Market Hypothesis in Conditionally Heteroskedastic Futures Markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(11), pages 1024-1045, November.
    17. Shuxin Guo, 2021. "Do futures lead the index under stress? Evidence from the 2015 Chinese market turmoil and its aftermath," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 91-110, January.
    18. Yaya, OlaOluwa S. & Tumala, Mohammed M. & Udomboso, Christopher G., 2016. "Volatility persistence and returns spillovers between oil and gold prices: Analysis before and after the global financial crisis," Resources Policy, Elsevier, vol. 49(C), pages 273-281.
    19. Nimitha John & Balakrishna Narayana, 2018. "Cointegration models with non Gaussian GARCH innovations," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 83-98, April.
    20. WenShwo Fang & Stephen M. Miller, 2002. "Dynamic Effects of Currency Depreciation on Stock Market Returns during the Asian Financial Crisis," Working papers 2002-31, University of Connecticut, Department of Economics.

    More about this item

    Keywords

    Vector autoregressive process; vector error correction model; cointegration; reduced rank estimation; maximum likelihood estimation; multivariate GARCH;
    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

    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:eui:euiwps:eco2009/42. 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: Cécile Brière (email available below). General contact details of provider: https://edirc.repec.org/data/deiueit.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.