Box-Jenkins and volatility models for Brazilian ‘Selic’ interest and currency rates

Abstract

The use of statistical models in the analysis of macroeconomic variables is of principal importance since these models support the economic theory, as well as represent the actual behaviour of these variables. In this context, this research has as objective to describe the behaviour of Brazilian SELIC interest rates and foreign exchange from January 1974 to February 2014 and from January 1980 to February 2014, respectively. To accomplish this objective the Box-Jenkins methodology was used, where the analysis of residues showed the presence of heteroscedasticity. Then joint modelling was used to estimate the mean process by an ARIMA and the conditional variance by ARCH, GARCH, TARCH, EGARCH models. The results obtained showed SELIC interest rate series, was modelled by an ARIMA (1,1,1)-EGARCH (3, 1, 1) and, to the exchange rate the modelled fitted was an ARIMA(0,1,1)-EGARCH(1,1,1). It is evidenced through these models that there is asymmetry in the variables, yet there was the leverage effect. In addition, the volatility of these series in the context of Brazilian economic scenario revel the face of external and internal crises in the periods examined. So, the models fitted effectively captured the Brazilian economic behaviour during the period comprehended from 80´s to 90´s showing the mid degree of persistence of shocks like bad and good news, aiding in understanding the performance of these variables providing decision-making to managers, to act in long and short term.