Scandinavian Working Papers in Economics
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Sveriges Riksbank (Central Bank of Sweden) Working Paper Series, Sveriges Riksbank (Central Bank of Sweden)

No 309:
Score Driven Exponentially Weighted Moving Averages and Value-at-Risk Forecasting

André Lucas () and Xin Zhang ()

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.

Keywords: dynamic volatilities; dynamic higher-order moments; integrated generalized autoregressive score models; Exponentially Weighted Moving Average (EWMA); Value-at-Risk (VaR); (follow links to similar papers)

JEL-Codes: C51; C52; C53; G15; (follow links to similar papers)

41 pages, September 1, 2015

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