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Distributional tests in multivariate dynamic models with Normal and Student t innovations

Author

Listed:
  • Javier Mencía

    (Banco de España)

  • Enrique Sentana

    (CEMFI)

Abstract

We derive Lagrange Multiplier and Likelihood Ratio specifi cation tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange Multiplier-type tests into skewness and kurtosis components, from which we obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the Likelihood Ratio test, whose asymptotic distribution we provide. We conduct detailed Monte Carlo exercises to study our proposed tests in finite samples. Finally, we present an empirical application to ten US sectoral stock returns, which indicates that their conditional distribution is mildly asymmetric and strongly leptokurtic.

Suggested Citation

  • Javier Mencía & Enrique Sentana, 2009. "Distributional tests in multivariate dynamic models with Normal and Student t innovations," Working Papers 0929, Banco de España.
    • Handle: RePEc:bde:wpaper:0929
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • 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

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