Fractional differentiation and its use in machine learning

Abstract

This article covers the implementation of fractional (non-integer order) differentiation on real data of four datasets based on stock prices of main international stock indexes: WIG 20, S&P 500, DAX and Nikkei 225. This concept has been proposed by Lopez de Prado [5] to find the most appropriate balance between zero differentiation and fully differentiated time series. The aim is making time series stationary while keeping its memory and predictive power. In addition, this paper compares fractional and classical differentiation in terms of the effectiveness of artificial neural networks. Root mean square error (RMSE) and mean absolute error (MAE) are employed in this comparison. Our investigations have determined the conclusion that fractional differentiation plays an important role and leads to more accurate predictions in case of ANN.