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Maximum likelihood estimation of score-driven models with dynamic shape parameters : an application to Monte Carlo value-at-risk

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Abstract

Dynamic conditional score (DCS) models with time-varying shape parameters provide a exible method for volatility measurement. The new models are estimated by using the maximum likelihood (ML) method, conditions of consistency and asymptotic normality of ML are presented, and Monte Carlo simulation experiments are used to study the precision of ML. Daily data from the Standard & Poor's 500 (S&P 500) for the period of 1950 to 2017 are used. The performances of DCS models with constant and dynamic shape parameters are compared. In-sample statistical performance metrics and out-of-sample value-at-risk backtesting support the use of DCS models with dynamic shape.

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  • Ayala, Astrid & Blazsek, Szabolcs, 2019. "Maximum likelihood estimation of score-driven models with dynamic shape parameters : an application to Monte Carlo value-at-risk," UC3M Working papers. Economics 28638, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:28638
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    1. F. Blasques & S. J. Koopman & A. Lucas, 2015. "Information-theoretic optimality of observation-driven time series models for continuous responses," Biometrika, Biometrika Trust, vol. 102(2), pages 325-343.
    2. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
    3. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    4. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    6. Creal, Drew & Koopman, Siem Jan & Lucas, André, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 552-563.
    7. John W. Galbraith, 2004. "Circuit Breakers and the Tail Index of Equity Returns," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 109-129.
    8. Tim Bollerslev & George Tauchen & Hao Zhou, 2009. "Expected Stock Returns and Variance Risk Premia," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4463-4492, November.
    9. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    10. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    11. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024, October.
    12. Tim Bollerslev & Viktor Todorov, 2011. "Estimation of Jump Tails," Econometrica, Econometric Society, vol. 79(6), pages 1727-1783, November.
    13. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Bryan Kelly & Hao Jiang, 2014. "Editor's Choice Tail Risk and Asset Prices," The Review of Financial Studies, Society for Financial Studies, vol. 27(10), pages 2841-2871.
    16. Escanciano, J. Carlos & Lobato, Ignacio N., 2009. "An automatic Portmanteau test for serial correlation," Journal of Econometrics, Elsevier, vol. 151(2), pages 140-149, August.
    17. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    18. Szabolcs Blazsek & Han-Chiang Ho & Su-Ping Liu, 2018. "Score-driven Markov-switching EGARCH models: an application to systematic risk analysis," Applied Economics, Taylor & Francis Journals, vol. 50(56), pages 6047-6060, December.
    19. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
    20. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    21. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    22. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    23. Bollerslev, Tim & Todorov, Viktor, 2014. "Time-varying jump tails," Journal of Econometrics, Elsevier, vol. 183(2), pages 168-180.
    24. Francisco Blasques & Paolo Gorgi & Siem Jan Koopman & Olivier Wintenberger, 2016. "Feasible Invertibility Conditions and Maximum Likelihood Estimation for Observation-Driven Models," Tinbergen Institute Discussion Papers 16-082/III, Tinbergen Institute.
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    Cited by:

    1. Ayala Astrid & Blazsek Szabolcs & Escribano Alvaro, 2023. "Anticipating extreme losses using score-driven shape filters," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 27(4), pages 449-484, September.
    2. Blazsek, Szabolcs & Licht, Adrian, 2019. "Markov-switching score-driven multivariate models: outlier-robust measurement of the relationships between world crude oil production and US industrial production," UC3M Working papers. Economics 29030, Universidad Carlos III de Madrid. Departamento de Economía.

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    More about this item

    Keywords

    Dynamic Conditional Score Models;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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