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Testing Constancy of the Error Covariance Matrix in Vector Models against Parametric Alternatives using a Spectral Decomposition

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  • Yukai Yang

    (Université catholique de Louvain)

Abstract

I consider multivariate (vector) time series models in which the error covariance matrix may be time-varying. I derive a test of constancy of the error covariance matrix against the alternative that the covariance matrix changes over time. I design a new family of Lagrange-multiplier tests against the alternative hypothesis that the innovations are time-varying according to several parametric specifications. I investigate the size and power properties of these tests and find that the test with smooth transition specification has satisfactory size properties. The tests are informative and may suggest to consider multivariate volatility modelling.

Suggested Citation

  • 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.
    • Handle: RePEc:aah:create:2014-11
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    References listed on IDEAS

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    1. Eklund, Bruno & Terasvirta, Timo, 2007. "Testing constancy of the error covariance matrix in vector models," Journal of Econometrics, Elsevier, vol. 140(2), pages 753-780, October.
    2. 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.
    3. Timo Teräsvirta & Yukai Yang, 2014. "Specification, Estimation and Evaluation of Vector Smooth Transition Autoregressive Models with Applications," CREATES Research Papers 2014-08, Department of Economics and Business Economics, Aarhus University.
    4. Lanne, Markku & Lütkepohl, Helmut & Maciejowska, Katarzyna, 2010. "Structural vector autoregressions with Markov switching," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 121-131, February.
    5. Terasvirta, Timo & Yang, Yukai, 2014. "Linearity and misspecification tests for vector smooth transition regression models," LIDAM Discussion Papers CORE 2014061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Markku Lanne & Helmut Lütkepohl, 2008. "Stock Prices and Economic Fluctuations: A Markov Switching Structural Vector Autoregressive Analysis," CESifo Working Paper Series 2407, CESifo.
    7. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    8. 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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    1. repec:hum:wpaper:sfb649dp2014-031 is not listed on IDEAS
    2. Terasvirta, Timo & Yang, Yukai, 2014. "Specification, estimation and evaluation of vector smooth transition autoregressive models with applications," LIDAM Discussion Papers CORE 2014062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with smooth transition in variances," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 43-57.
    4. 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.
    5. Lütkepohl, Helmut & Netésunajev, Aleksei, 2014. "Structural vector autoregressions with smooth transition in variances: The interaction between US monetary policy and the stock market," SFB 649 Discussion Papers 2014-031, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. Maria Bolboaca & Sarah Fischer, 2019. "News Shocks: Different Effects in Boom and Recession?," Working Papers 19.01, Swiss National Bank, Study Center Gerzensee.
    7. 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.

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    More about this item

    Keywords

    Covariance constancy; Error covariance structure; Lagrange multiplier test; Spectral decomposition; Auxiliary regression; 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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