VOLATILITY FORECASTING AFTER REMOVING THE NOISE: DOES IT REALLY PAY OFF?

Abstract

The analysis in this paper represents the first attempt to examine whether the forecasting performance of one of the GARCH models can be improved after removing the noise from the stock market returns. Doing the analysis on eight developed stock markets helps in providing reliable results that can be generalized to more stock markets. This paper then examines the ability of GARCH models to forecast stock return volatility under a range of statistical forecasts. We specifically employ the multiscale-based approach, namely the maximum overlap discrete wavelet transformation, to remove the noisy data from the return series. Based on related theoretical literature, we assume that noise trading makes the forecasting performance more misleading, especially at the short-term horizon. Our particular interest then is whether wavelet de-noising of the data before estimation affects the ability of the models to provide accurate forecasts at a short investment horizon. To de-noise the data, we use soft thresholding and Stein’s Unbiased Risk Estimator to obtain the decomposition level-based threshold limit. Our key results demonstrate that de-noising returns improves the accuracy of volatility forecasts regardless of whether we used statistical metrics or tests of equal predictive accuracy. Moreover, 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.