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Testing constancy of the error covariance matrix in vector models

Author

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  • Eklund, Bruno

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    (Dept. of Economic Statistics, Stockholm School of Economics)

Abstract

This paper contains a Lagrange multiplier test of the hypothesis that the covariance matrix of a multivariate time series model is constant over time. It is further assumed that under the alternative, the error variances are time-varying whereas the correlation remain constant over time. Under the parameterized alternative hypothesis the variance may change continuously as a function of time or some observable stochastic variables.

Suggested Citation

  • Eklund, Bruno & Teräsvirta, Timo, 2003. "Testing constancy of the error covariance matrix in vector models," SSE/EFI Working Paper Series in Economics and Finance 549, Stockholm School of Economics, revised 18 Jan 2006.
    • Handle: RePEc:hhs:hastef:0549
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    References listed on IDEAS

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    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    3. Tse, Y. K., 2000. "A test for constant correlations in a multivariate GARCH model," Journal of Econometrics, Elsevier, vol. 98(1), pages 107-127, September.
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    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    7. Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Research Paper Series 168, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    9. Marcelo C. Medeiros & Alvaro Veiga, 2003. "Diagnostic Checking in a Flexible Nonlinear Time Series Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 461-482, July.
    10. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521839198.
    11. 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.
    12. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871.
    13. 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.
    14. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Citations

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    Cited by:

    1. Paul Catani & Timo Teräsvirta & Meiqun Yin, 2017. "A Lagrange multiplier test for testing the adequacy of constant conditional correlation GARCH model," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 599-621, October.
    2. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    3. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, March.
    4. Yukai Yang, 2014. "Testing Constancy of the Error Covariance Matrix in Vector Models against Parametric Alternatives using a Spectral Decomposition," CREATES Research Papers 2014-11, Department of Economics and Business Economics, Aarhus University.
    5. Holt, Matthew T. & Teräsvirta, Timo, 2020. "Global hemispheric temperatures and co-shifting: A vector shifting-mean autoregressive analysis," Journal of Econometrics, Elsevier, vol. 214(1), pages 198-215.
    6. Catani, P.S. & Ahlgren, N.J.C., 2017. "Combined Lagrange multiplier test for ARCH in vector autoregressive models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 62-84.
    7. Annastiina Silvennoinen & Timo Teräsvirta, 2017. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    8. Jian Kang & Johan Stax Jakobsen & Annastiina Silvennoinen & Timo Teräsvirta & Glen Wade, 2022. "A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-Varying GARCH Model," Econometrics, MDPI, vol. 10(3), pages 1-41, August.

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    More about this item

    Keywords

    error covariance structure; Lagrange multiplier test; model misspecification; Monte Carlo simulation;
    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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