Score Driven Exponentially Weighted Moving Averages and Value-at-Risk Forecasting
Riksbank Research Paper Series No. 133
Sveriges Riksbank Working Paper Series No. 309
35 Pages Posted: 22 Dec 2015
There are 2 versions of this paper
Score Driven Exponentially Weighted Moving Averages and Value-at-Risk Forecasting
Date Written: September 2015
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(TM) 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 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.
Keywords: dynamic volatilities, dynamic higher-order moments, integrated generalized autoregressive score models, Exponentially Weighted Moving Average (EWMA), Value-at-Risk (VaR)
JEL Classification: C51, C52, C53, G15
Suggested Citation: Suggested Citation