Physica A 492 (2018) 1431–1438 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Long-term correlations and cross-correlations in IBovespa and constituent companies Neílson F. de Lima a , Leonardo H.S. Fernandes c , Jader S. Jale c , Paulo S.G. de Mattos Neto b , Tatijana Stošić c , Borko Stošić c , Tiago A.E. Ferreira c , * a Federal Institute of Science Education and Technology, Rio Grande do Norte, Brazil b Center of Informatics, Federal University of Pernambuco, Recife, Brazil c Department of Statistics and Informatics, Federal Rural University of Pernambuco, Recife, Brazil highlights • Applications of DFA and DCCA analysis to the Brazilian stock market and its companies. • The results found a long term correlation between the IBovespa and the its companies. • The experimental results were divided by productive sectors of the Brazilian market. • A comparison between the USA and Brazilian Markets was done. article info Article history: Received 3 July 2017 Received in revised form 27 September 2017 Available online 22 November 2017 Keywords: IBovespa DFA DCCA Market efficiency Correlation abstract We study auto-correlations and cross-correlations of IBovespa index and its constituent companies. We use Detrended Fluctuation Analysis (DFA) to quantify auto-correlations and Detrended Cross-Correlation Analysis (DCCA) to quantify cross-correlations in absolute returns of daily closing prices of IBovespa and the individual companies. We find persistent long-term correlations and cross-correlations which are weaker than those found for USA market. Our results indicate that market indices of developing markets exhibit weaker coupling with its constituents than for mature developed markets. © 2017 Elsevier B.V. All rights reserved. 1. Introduction The IBovespa, the Bovespa’s index is the main indicator of mean share prices in the Brazilian stock market. The method used for this index is based on the most traded financial assets in last months and current value represents the amount of cash on a theoretical portfolio. Currently, the IBovespa is comprised of fifty eight companies [1]. The behavior of IBovespa appears as a useful tool to check the level of economic stability. A volatile behavior of prices results in nervous investors, leading to slower economic growth and lower leaving standards. Since the emerge of econophysics, the new subfield that uses methods of statistical physics to analyze financial indices [2], long-term correlations and cross-correlations in financial temporal series were extensively studied. The reported results include stock market indices, trade volume, prices of individual stocks, commodities, currency exchange rates and interest * Corresponding author. E-mail address: tiago.espinola@ufrpe.br (T.A.E. Ferreira). https://doi.org/10.1016/j.physa.2017.11.070 0378-4371/© 2017 Elsevier B.V. All rights reserved.