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

Authors: João Nunes De Mendonça Neto; Luiz Paulo Lopes Fávero; Renata Turola Takamatsu

Addresses: School of Economics, Business and Accounting, Department of Accounting, University of São Paulo, Rua Fernando Tuy, 318 – Ap. 201 – Pituba, Salvador – BA, Brazil ' School of Economics, Business and Accounting, Department of Accounting, University of São Paulo, Av. Prof. Luciano Gualberto, 908 – FEA 3 – sala 211 – Cidade Universitária, São Paulo – SP, Brazil ' Department of Accounting, Federal University of Minas Gerais, Av. Antônio Carlos, 6627, FACE/UFMG, sala 2042 – Campus Universitário, Belo Horizonte – MG, Brazil

Abstract: 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.

Keywords: Hurst exponent; fractals; ANNs; artificial neural networks; time series forecasting; financial assets.

DOI: 10.1504/IJDS.2018.090625

International Journal of Data Science, 2018 Vol.3 No.1, pp.29 - 49

Received: 27 Aug 2015
Accepted: 04 Jan 2016

Published online: 19 Mar 2018 *

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