Statistical properties of the return series of principal Brazilian stocks

This paper studies the returns of six Brazilian stocks, chosen among the most liquid and from different economic sectors. Stationarity, unconditional distribution and independence are studied, and the conclusion is that the series are stationary, have non-normal (leptokurtic) distribution and are dependent. Stationarity is studied with the help of the ADF test, of the coefficients of GARCH models adjusted to the data, of bicorrelation coefficients and of locally weighted regression. Normality was rejected using the Jarque and Bera test. Dependence (linear and non-linear) was indicated by the autocorrelations of returns and squared returns: ARMA, exponential smoothing, and GARCH models are used to try to capture the dependence, but the BDS tests of model's residuals show that they do not represent well the data generating process.