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Qml inference for volatility models with covariates

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  • Francq, Christian
  • Thieu, Le Quyen

Abstract

The asymptotic distribution of the Gaussian quasi-maximum likelihood estimator (QMLE) is obtained for a wide class of asymmetric GARCH models with exogenous covariates. The true value of the parameter is not restricted to belong to the interior of the parameter space, which allows us to derive tests for the significance of the parameters. In particular, the relevance of the exogenous variables can be assessed. The results are obtained without assuming that the innovations are independent, which allows conditioning on different information sets. Monte Carlo experiments and applications to financial series illustrate the asymptotic results. In particular, an empirical study demonstrates that the realized volatility is an helpful covariate for predicting squared returns, but does not constitute an ideal proxy of the volatility.

Suggested Citation

  • Francq, Christian & Thieu, Le Quyen, 2015. "Qml inference for volatility models with covariates," MPRA Paper 63198, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:63198
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    References listed on IDEAS

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    More about this item

    Keywords

    APARCH model augmented with explanatory variables; Boundary of the parameter space; Consistency and asymptotic distribution of the Gaussian quasi-maximum likelihood estimator; GARCH-X models; Power-transformed and Threshold GARCH with exogenous covariates;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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