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Score Driven exponentially Weighted Moving Average and Value-at-Risk Forecasting

Author

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  • André Lucas

    (VU University Amsterdam, the Netherlands)

  • Xin Zhang

    (Sveriges Riksbank, 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 RiskMetrics approach. We update parameters using the score of the forecasting distribution. This allows the parameter dynamics to adapt automatically to any non-normal data features and robustifies 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

  • André Lucas & Xin Zhang, 2014. "Score Driven exponentially Weighted Moving Average and Value-at-Risk Forecasting," Tinbergen Institute Discussion Papers 14-092/IV/DSF77, Tinbergen Institute, revised 09 Sep 2015.
  • Handle: RePEc:tin:wpaper:20140092
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    References listed on IDEAS

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    More about this item

    Keywords

    dynamic volatilities; time varying higher order moments; integrated generalized autoregressive score models; Exponential 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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