Hurst exponent, fractals and neural networks for forecasting financial asset returns in Brazil

Our scope is to verify the existence of a relationship between long-term memory in fractal time series and the prediction error of financial asset returns obtained by artificial neural networks (ANNs). We expect that the fractal time series with larger memory can achieve predictions with lower error, since the correlation between elements of the series favours the quality of ANN prediction. As a long-term memory measure, the Hurst exponent of each time series was calculated, and the root mean square error (RMSE) produced by ANN in each time series was used to measure the prediction error. Hurst exponent computation was conducted through the rescaled range analysis (R/S) algorithm. The ANN's architecture used time-lagged feedforward neural networks (TLFN), with backpropagation supervised learning process and gradient descent for error minimisation. Brazilian financial assets traded at BM%FBovespa, specifically public companies shares and real estate investment funds were considered.