Modelagem da volatilidade dos retornos dos preços da arroba do boi gordo em Mato Grosso via modelos ARCH-GARCH

Abstract

The beef cattle chain has been widely developed over the years and, with that, the need for tools that assist in the cattleman's decision-making at the time of selling the animal has been increasingly important. As it is a sector in which several parameters can impact the pricing of live cattle, the analysis of the volatility of the returns of the arroba prices used for the financial market can be a way for the producer to prepare for market fluctuations. Thus, the main objec tive of the present study is to analyze the applications of the ARCH-GARCH model (General ized Conditional Autoregressive Heteroscedasticity) to examine the volatility of the daily re turns of the prices of the arroba of cattle that comprises the period from January 2008 to August 2008. 2022 The first step was to analyze whether the generated returns are correlated through the graphical visualization of the FAC and FACP. Then, the L-Jung-Box test was performed to verify the existence of data autocorrelation. As the returns are correlated and stationary, the ARMA model was adjusted to remove autocorrelation from the data. The results were obtained through the ADF and KPSS test. In both tests it was possible to infer that the series of returns was stationary. Thus, it was necessary to fit an ARMA model before the GARCH model in the data series. Then the GARCH model was adjusted, which after several tests performed, the most suitable model to model the high persistence in volatility was the GARCH (1,1) with Student's t innovations. In the GARCH model found, the sum of the coefficients α_1 and β_1 indicated that the persistence of volatility shocks takes longer to disappear. The results of the application of the Ljung-Box test to the residuals and the squares of the standardized residuals, as well as the result of the ARCH-LM test, demonstrated that the model is well adjusted to the daily returns of the live cattle price.