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Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown

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  • Sucarrat, Genaro
  • Grønneberg, Steffen
  • Escribano, Alvaro

Abstract

A general framework for the estimation and inference in univariate and multivariate Generalised log-ARCH-X (i.e. log-GARCH-X) models when the conditional density is unknown is proposed. The framework employs (V)ARMA-X representations and relies on a bias-adjustment in the log-volatility intercept. The bias is induced by (V)ARMA estimators, but the remaining parameters can be estimated in a consistent and asymptotically normal manner by usual (V)ARMA methods. An estimator of the bias and a closed-form expression for the asymptotic variance is derived. Adding covariates and/or increasing the dimension of the model does not change the structure of the problem, so the univariate bias-adjustment procedure is applicable not only in univariate log-GARCH-X models estimated by the ARMA-X representation, but also in multivariate log-GARCH-X models estimated by VARMA-X representations. Extensive simulations verify the properties of the log-moment estimator, and an empirical application illustrates the usefulness of the methods.

Suggested Citation

  • Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
  • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:582-594
    DOI: 10.1016/j.csda.2015.12.005
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    Cited by:

    1. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    2. Holger Fink & Andreas Fuest & Henry Port, 2018. "The Impact of Sovereign Yield Curve Differentials on Value-at-Risk Forecasts for Foreign Exchange Rates," Risks, MDPI, Open Access Journal, vol. 6(3), pages 1-19, August.
    3. Francq, Christian & Sucarrat, Genaro, 2017. "An equation-by-equation estimator of a multivariate log-GARCH-X model of financial returns," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 16-32.
    4. Sucarrat, Genaro & Escribano, Álvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," UC3M Working papers. Economics we1321, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Escribano, Alvaro & Sucarrat, Genaro, 2018. "Equation-by-equation estimation of multivariate periodic electricity price volatility," Energy Economics, Elsevier, vol. 74(C), pages 287-298.
    6. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 129-154.
    7. Christian Francq & Olivier Wintenberger & Jean-Michel Zakoïan, 2018. "Goodness-of-fit tests for Log-GARCH and EGARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 27-51, March.

    More about this item

    Keywords

    Log-GARCH-X; ARMA-X; Multivariate log-GARCH-X; VARMA-X; Volatility;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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