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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

Exponential models of Autoregressive Conditional Heteroscedasticity (ARCH) enable richer dynamics (e.g. contrarian or cyclical), provide greater robustness to jumps and outliers, and guarantee the positivity of volatility. The latter is not guaranteed in ordinary ARCH models, in particular when additional exogenous or predetermined variables ("X") are included in the volatility specification. Here, we propose estimation and inference methods for univariate and multivariate Generalised log-ARCH-X (i.e. log-GARCH-X) models when the conditional density is not known via (V)ARMA-X representations. The multivariate specification allows for volatility feedback across equations, and time-varying correlations can be fitted in a subsequent step. Finally, our empirical applications on electricity prices show that the model-class is particularly useful when the X-vector is high-dimensional.

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  • Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2013. "Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown," MPRA Paper 49344, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:49344
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    Cited by:

    1. Raffaele Mattera & Philipp Otto, 2023. "Network log-ARCH models for forecasting stock market volatility," Papers 2303.11064, arXiv.org.
    2. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    3. Boubacar Maïnassara, Y. & Kadmiri, O. & Saussereau, B., 2022. "Estimation of multivariate asymmetric power GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    4. Philipp Otto, 2022. "A Multivariate Spatial and Spatiotemporal ARCH Model," Papers 2204.12472, arXiv.org.
    5. 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, vol. 6(3), pages 1-19, August.
    6. 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.
    7. 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.
    8. Escribano, Alvaro & Sucarrat, Genaro, 2018. "Equation-by-equation estimation of multivariate periodic electricity price volatility," Energy Economics, Elsevier, vol. 74(C), pages 287-298.
    9. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    10. James Reade & Genaro Sucarrat, 2016. "General-to-Specific (GETS) Modelling And Indicator Saturation With The R Package Gets," Economics Series Working Papers 794, University of Oxford, Department of Economics.
    11. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.
    12. Christian M. Hafner & Dimitra Kyriakopoulou, 2021. "Exponential-Type GARCH Models With Linear-in-Variance Risk Premium," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 589-603, March.
    13. Sebastian Letmathe & Yuanhua Feng & André Uhde, 2021. "Semiparametric GARCH models with long memory applied to Value at Risk and Expected Shortfall," Working Papers CIE 141, Paderborn University, CIE Center for International Economics.
    14. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 129-154.
    15. Sucarrat, Genaro, 2020. "Identification of Volatility Proxies as Expectations of Squared Financial Return," MPRA Paper 101953, University Library of Munich, Germany.
    16. Pourkhanali, Armin & Tafakori, Laleh & Bee, Marco, 2023. "Forecasting Value-at-Risk using functional volatility incorporating an exogenous effect," International Review of Financial Analysis, Elsevier, vol. 89(C).
    17. 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.
    18. Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    19. Bonnier, Jean-Baptiste, 2022. "Forecasting crude oil volatility with exogenous predictors: As good as it GETS?," Energy Economics, Elsevier, vol. 111(C).
    20. Sucarrat, Genaro, 2021. "Identification of volatility proxies as expectations of squared financial returns," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1677-1690.

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    More about this item

    Keywords

    ARCH; exponential GARCH; log-GARCH; ARMA-X; Multivariate GARCH;
    All these keywords.

    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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