Box-Jenkins and Volatility Models for Brazilian ‘Selic’ Interest and Currency Rates

Abstract

The use of statistical models in theanalysis of macroeconomic variables is of principalimportance since these models support the economictheory, as well as represent the actual behaviour ofthese variables. In this context, this research has asobjective to describe the behaviour of Brazilian SELICinterest rates and foreign exchange from January 1974to February 2014 and from January 1980 to February2014, respectively. To accomplish this objective the Box-Jenkins methodology was used, where the analysis ofresidues showed the presence of heteroscedasticity.Then joint modelling was used to estimate the meanprocess by an ARIMA and the conditional variance byARCH, GARCH, TARCH, EGARCH models. Theresults obtained showed SELIC interest rate series, wasmodelled by an ARIMA (1,1,1)-EGARCH (3, 1, 1) and,to the exchange rate the modelled fitted was anARIMA(0,1,1)-EGARCH(1,1,1). It is evidenced throughthese models that there is asymmetry in the variables,yet there was the leverage effect. In addition, thevolatility of these series in the context of Brazilianeconomic scenario revel the face of external andinternal crises in the periods examined. So, the modelsfitted effectively captured the Brazilian economicbehaviour during the period comprehended from 80´sto 90´s showing the mid degree of persistence of shockslike bad and good news, aiding in understanding theperformance of these variables providing decisionmakingto managers, to act in long and short term.