Volatility and Value-at-Risk Forecasting: Does Wavelet De-Noising Help?

Abstract

This paper examines the ability of different GARCH models to forecast stock return volatility under a range of forecast metrics, including both statistical and economic evaluation. In particular, we are interested in whether wavelet de-noising of the data prior to estimation affects the ability of the models to provide accurate forecasts. In de-noising the data, we consider soft thresholding approach along with the Stein’s Unbiased Risk Estimator to get the decomposition level-based threshold limit. Our key results demonstrate that de-noising returns improves the accuracy of volatility forecasts regardless of whether we use statistical metrics, tests of equal predictive accuracy or a VaR procedure. In terms of a particular volatility model, the asymmetric GARCH approach tends to be preferred although this result is not universal. Indeed, the central result from our analysis is that the process of de-noising is more important than the specific model. Furthermore, when considering VaR forecasting, wavelet de-noising is found to be more important at the key 99% level compared to the 95% level.