Generalized Value at Risk Forecasting

In this paper, using estimating function approach, a new optimal volatility estimator is introduced, and, based on the recursive form of the estimator, a data-driven generalized EWMA model for VaR forecast is proposed. An appropriate data-driven model for volatility is identified by the relationship between the absolute deviation and the standard deviation for symmetric distributions with finite variance. It is shown that the asymptotic variance of the proposed volatility estimator is smaller than that of conventional estimators and is more appropriate for financial data with larger kurtosis. For IBM, Microsoft, and Apple stocks the proposed method is used to identify the model, estimate the volatility, and obtain VaR forecasts