# 14-092/IV/DSF77 (2014-07-22; 2015-09-09)

André Lucas, VU University Amsterdam, the Netherlands; Xin Zhang, Sveriges Riksbank, Sweden
dynamic volatilities, time varying higher order moments, integrated generalized autoregressive score models, Exponential Weighted Moving Average (EWMA), Value-at-Risk (VaR)
JEL codes:
C51, C52, C53, G15

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.