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

We present a simple new methodology to allow for time variation in volatilities using a recursive updating scheme similar to the familiar RiskMetrics approach. We update parameters using the score of the forecasting distribution rather than squared lagged observations. This allows the parameter dynamics to adapt automatically to any non-normal data features and robustifies the subsequent volatility estimates. Our new approach nests several extensions to the exponentially weighted moving average (EWMA) scheme as proposed earlier. Our approach also easily handles extensions to dynamic higher-order moments or other choices of the preferred forecasting distribution. We apply our method to Value-at-Risk forecasting with Student's t distributions and a time varying degrees of freedom parameter and show that the new method is competitive to or better than earlier methods for volatility forecasting of individual stock returns and exchange rates.