Stability of stock prices in the Brazilian capital market: a study applying neural networks and the Lyapunov exponent

Abstract

In this article, we study the stability of the market price of stocks for two categories of companies, referred to as industrial (IND) and other sectors (OSE), from January 2, 1995 to January 2, 2008. In other words, we examine the stability of market prices for the period before the 2008 crisis, triggered by the US subprime securities. We analyze the implications of the stability of the process of generating a return through rationality paradigms. The verification of stability was conducted using Lyapunov exponents. Results are presented on the stability of prices for two categories of companies: industrial concerns, comprising Acesita, Ambev, Aracruz, Braskem, Duratex, Fosfertil, Gerdau, Klabin, Randon, Sadia, Sid Nacional, Souza Cruz, Unipar, Usiminas and VCP, and enterprises in the other sectors category, comprising Ampla Energy, Bradesco, Brasil Telecom, Cemig, Eletrobras, Eletrobrás, Itaubanco, Itaúsa, JB Duarte, Pronor, Besc, Alpha Financeira and Inepar. A dispersion diagram of the logarithm of prices without trends vs. the returns of these two categories (or portfolios) showed a chaotic pattern of stock prices, indicating the presence of nonlinearity. However, the calculation of the Lyapunov exponents resulted in negative values. This indicates that the fluctuations of the 30 companies analyzed result from diffusion processes rather than from nonlinear dynamics. The rationality of the behavior of prices is studied by checking the residues generated from estimates of ARMA and NAIVE models and feedforward neural networks.