Predictive performance of denoising algorithms in S&P 500 and Bitcoin returns

This paper aims to investigate the effectiveness of both the Hankel matrix and the Wavelet denoise methods to address the issue of denoising volatility in datasets, specifically squared returns, and to enhance the accuracy of post-sample forecasting. When converting data from levels to volatility, noise levels are amplified, and the forecasting models suffer from structural bias, leading to reduced accuracy gains. The main challenge in denoising operations is preserving systemic impulses while extracting sporadic and unpredictable components. While conventional denoising algorithms struggle to distinguish systemic patterns from noise, the Hankel matrix approach surpasses them in performance, resulting in improved predictive accuracy. Additionally, this paper explores the Wavelet denoise method, which is found to be less effective than the Hankel matrix approach for GARCH models. The empirical work showcases the denoising process and the accuracy improvements achieved in various datasets for GARCH models. By implementing the Hankel matrix approach, simulations reveal a notable accuracy gain of over 10%.