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The Bovespa Index is the most important indicator of the average performance of quotations on the Brazilian stock market, portraying the behavior of the main securities traded on the Bovespa. The Petrobras Index refers to Petrobras quotations on the São Paulo Stock Exchange (Bovespa). In view of the expressiveness of these indices, the objective of this work will be to perform a univariate and multivariate temporal analysis of the series of returns of Petrobrás and Ibovespa in two periods. The first period is comprised between 2005 and 2015, while the second between 2015 and 2019. This division was intended to divide the pre and post crisis periods in the face of complaints of corruption against Petrobras, which caused a greater variation in liquidity in the company's shares. The survey is ongoing and only the analysis of the first period is complete. The series data were taken from the IPEADATA website (ipeadata.gov.br), then deflated, and then their returns were calculated using software R. This is done in two steps. In the first, the data are modeled using the ARIMA model, and in the second, the GARCH is fitted to the squared residues. For the Bovespa index series, an ARIMA (3.0.3) and then GARCH (1.1) were fitted. For the Petrobras series of returns, first, an incomplete ARMA was fittted with the autoregressive parameters of significant order 6 and the order 3 of moving averages also statistically significant. The volatility, in this case, was also fitted by a GARCH (1.1). The rates of the two returns were useful. A multivariate analysis indicated that, during the analyzed lag period, the Petrobras index did not directly influence the Bovespa index, although in the analyzed period it was chosen before the denunciation and corruption scandal. After analyzing the second period, a comparison will be made between the fits.
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