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Score-driven exponentially weighted moving averages and Value-at-Risk forecasting

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  • Lucas, André
  • Zhang, Xin

Abstract

We present a simple methodology for modeling the time variation in volatilities and other higher-order moments using a recursive updating scheme that is similar to the familiar RiskMetrics™ approach. The parameters are updated using the score of the forecasting distribution, which allows the parameter dynamics to adapt automatically to any non-normal data features, and increases the robustness of the subsequent estimates. The new approach nests several of the earlier extensions to the exponentially weighted moving average (EWMA) scheme. In addition, it can be extended easily to higher dimensions and alternative forecasting distributions. The method is applied to Value-at-Risk forecasting with (skewed) Student’s t distributions and a time-varying degrees of freedom and/or skewness parameter. We show that the new method is as good as or better than earlier methods for forecasting the volatility of individual stock returns and exchange rate returns.

Suggested Citation

  • Lucas, André & Zhang, Xin, 2016. "Score-driven exponentially weighted moving averages and Value-at-Risk forecasting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 293-302.
  • Handle: RePEc:eee:intfor:v:32:y:2016:i:2:p:293-302
    DOI: 10.1016/j.ijforecast.2015.09.003
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    9. Francisco Blasques & Siem Jan Koopman & André Lucas, 2014. "Information Theoretic Optimality of Observation Driven Time Series Models," Tinbergen Institute Discussion Papers 14-046/III, Tinbergen Institute.
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    13. André Lucas & Bernd Schwaab & Xin Zhang, 2014. "Conditional Euro Area Sovereign Default Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 271-284, April.
    14. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    15. Blasques, Francisco & Ji, Jiangyu & Lucas, André, 2016. "Semiparametric score driven volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 58-69.
    16. Schwert, G William, 1990. "Stock Volatility and the Crash of '87," Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 77-102.
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    18. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    19. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    20. Ardia, David & Hoogerheide, Lennart F., 2014. "GARCH models for daily stock returns: Impact of estimation frequency on Value-at-Risk and Expected Shortfall forecasts," Economics Letters, Elsevier, vol. 123(2), pages 187-190.
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    22. 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.
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    Cited by:

    1. Alexandros Gabrielsen & Axel Kirchner & Zhuoshi Liu & Paolo Zagaglia, 2015. "Forecasting Value-At-Risk With Time-Varying Variance, Skewness And Kurtosis In An Exponential Weighted Moving Average Framework," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 1-29.
    2. Andries C. van Vlodrop & Andre (A.) Lucas, 2018. "Estimation Risk and Shrinkage in Vast-Dimensional Fundamental Factor Models," Tinbergen Institute Discussion Papers 18-099/III, Tinbergen Institute.
    3. Ryoko Ito, 2016. "Asymptotic Theory for Beta-t-GARCH," Cambridge Working Papers in Economics 1607, Faculty of Economics, University of Cambridge.
    4. Gorgi, Paolo & Koopman, Siem Jan & Li, Mengheng, 2019. "Forecasting economic time series using score-driven dynamic models with mixed-data sampling," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1735-1747.
    5. Song, Shijia & Li, Handong, 2023. "A method for predicting VaR by aggregating generalized distributions driven by the dynamic conditional score," The Quarterly Review of Economics and Finance, Elsevier, vol. 88(C), pages 203-214.
    6. Liu, Wei & Semeyutin, Artur & Lau, Chi Keung Marco & Gozgor, Giray, 2020. "Forecasting Value-at-Risk of Cryptocurrencies with RiskMetrics type models," Research in International Business and Finance, Elsevier, vol. 54(C).
    7. André Lucas & Julia Schaumburg & Bernd Schwaab, 2019. "Bank Business Models at Zero Interest Rates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 542-555, July.
    8. Mauro Bernardi & Leopoldo Catania, 2016. "Comparison of Value-at-Risk models using the MCS approach," Computational Statistics, Springer, vol. 31(2), pages 579-608, June.
    9. Carlos Henrique Dias Cordeiro de Castro & Fernando Antonio Lucena Aiube, 2023. "Forecasting inflation time series using score‐driven dynamic models and combination methods: The case of Brazil," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 369-401, March.
    10. Anne Opschoor & André Lucas, 2019. "Time-varying tail behavior for realized kernels," Tinbergen Institute Discussion Papers 19-051/IV, Tinbergen Institute.
    11. Laporta, Alessandro G. & Merlo, Luca & Petrella, Lea, 2018. "Selection of Value at Risk Models for Energy Commodities," Energy Economics, Elsevier, vol. 74(C), pages 628-643.
    12. Catania, Leopoldo & Grassi, Stefano, 2022. "Forecasting cryptocurrency volatility," International Journal of Forecasting, Elsevier, vol. 38(3), pages 878-894.
    13. Opschoor, Anne & Lucas, André, 2023. "Time-varying variance and skewness in realized volatility measures," International Journal of Forecasting, Elsevier, vol. 39(2), pages 827-840.
    14. Ito, R., 2016. "Spline-DCS for Forecasting Trade Volume in High-Frequency Finance," Cambridge Working Papers in Economics 1606, Faculty of Economics, University of Cambridge.
    15. Bram van Os, 2023. "Information-Theoretic Time-Varying Density Modeling," Tinbergen Institute Discussion Papers 23-037/III, Tinbergen Institute.
    16. Arian, Hamid & Moghimi, Mehrdad & Tabatabaei, Ehsan & Zamani, Shiva, 2022. "Encoded Value-at-Risk: A machine learning approach for portfolio risk measurement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 500-525.
    17. Palumbo, D., 2021. "Testing and Modelling Time Series with Time Varying Tails," Cambridge Working Papers in Economics 2111, Faculty of Economics, University of Cambridge.
    18. David Ardia & Kris Boudt & Leopoldo Catania, 2016. "Generalized Autoregressive Score Models in R: The GAS Package," Papers 1609.02354, arXiv.org.
    19. Fuentes, Fernanda & Herrera, Rodrigo & Clements, Adam, 2023. "Forecasting extreme financial risk: A score-driven approach," International Journal of Forecasting, Elsevier, vol. 39(2), pages 720-735.
    20. Ching-Jui Tien & Chia-Sheng Tu & Ming-Tang Tsai, 2022. "Risk Assessment of User Aggregators in Demand Bidding Markets," Energies, MDPI, vol. 16(1), pages 1-14, December.
    21. Paul Labonne, 2020. "Capturing GDP nowcast uncertainty in real time," Papers 2012.02601, arXiv.org, revised Oct 2021.
    22. Rutger-Jan Lange & Andre Lucas & Arjen H. Siegmann, 2016. "Score-Driven Systemic Risk Signaling for European Sovereign Bond Yields and CDS Spreads," Tinbergen Institute Discussion Papers 16-064/IV, Tinbergen Institute.
    23. Semeyutin, Artur & O’Neill, Robert, 2019. "A brief survey on the choice of parameters for: “Kernel density estimation for time series data”," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).

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    More about this item

    Keywords

    Dynamic volatilities; Dynamic higher-order moments; Integrated generalized autoregressive score models; Exponentially Weighted Moving Average (EWMA); Value-at-Risk (VaR);
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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