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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. 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.
    2. Markku Lanne & Helmut Luetkepohl, 2008. "Stock Prices and Economic Fluctuations: A Markov Switching Structural Vector Autoregressive Analysis," Economics Working Papers ECO2008/29, European University Institute.
    3. Timo Teräsvirta & Yukai Yang, 2014. "Linearity and Misspecification Tests for Vector Smooth Transition Regression Models," CREATES Research Papers 2014-04, Department of Economics and Business Economics, Aarhus University.
    4. Eklund, Bruno & Terasvirta, Timo, 2007. "Testing constancy of the error covariance matrix in vector models," Journal of Econometrics, Elsevier, pages 753-780.
    5. 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.
    6. Silvia Sgherri & Bertrand Gruss, 2009. "The Volatility Costs of Procyclical Lending Standards; An Assessment Using a Dsge Model," IMF Working Papers 09/35, International Monetary Fund.
    7. 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.
    8. Markku Lanne & Helmut Luetkepohl, 2008. "Stock Prices and Economic Fluctuations: A Markov Switching Structural Vector Autoregressive Analysis," Economics Working Papers ECO2008/29, European University Institute.
    9. 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.
    10. 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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    Cited by:

    1. repec:eee:dyncon:v:84:y:2017:i:c:p:43-57 is not listed on IDEAS
    2. Helmut Lütkepohl & Aleksei Netsunajev, 2014. "Structural Vector Autoregressions with Smooth Transition in Variances - The Interaction Between U.S. Monetary Policy and the Stock Market," SFB 649 Discussion Papers SFB649DP2014-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. 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.

    More about this item

    Keywords

    Covariance constancy; Error covariance structure; Lagrange multiplier test; Spectral decomposition; Auxiliary regression; Model misspecification; Monte Carlo simulation;

    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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