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Score Driven Exponentially Weighted Moving Averages and Value-at-Risk Forecasting

Author

Listed:
  • Lucas, André

    (VU University Amsterdam and Tinbergen Institute)

  • Zhang, Xin

    (Research Department, Central Bank of Sweden)

Abstract

A simple methodology is presented for modeling time variation in volatilities and other higher-order moments using a recursive updating scheme similar to the familiar RiskMetricsTM approach. We update parameters using the score of the forecasting distribution. This allows the parameter dynamics to adapt automatically to any nonnormal data features and robusti es the subsequent estimates. The new approach nests several of the earlier extensions to the exponentially weighted moving average (EWMA) scheme. In addition, it can easily be extended 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 competitive to or better than earlier methods in forecasting volatility of individual stock returns and exchange rate returns.

Suggested Citation

  • Lucas, André & Zhang, Xin, 2015. "Score Driven Exponentially Weighted Moving Averages and Value-at-Risk Forecasting," Working Paper Series 309, Sveriges Riksbank (Central Bank of Sweden).
    • Handle: RePEc:hhs:rbnkwp:0309
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    References listed on IDEAS

    as
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    2. 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.
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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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