Modeling the exchange rate of the euro against the dollar using the ARCH/GARCH models

Abstract

The analysis of time series with conditional heteroskedasticity (changeable time variability, conditional variance instability, the phenomenon called volatility) is the main task of ARCH and GARCH models. The aim of these models is to calculate some of the volatility indicators needed for financial decisions. This paper examines the performance of generalized autoregressive conditional heteroscedasticity (GARCH) model in modeling the daily changes of the log exchange rate of the euro against the dollar. Several GARCH models have been applied for modeling the daily log exchange rate returns of the euro, with a different number of parameters. The characteristic of estimated GARCH models is that the obtained coefficients of lagged squared residuals and the conditional variance parameters in the equation of conditional variance have a strong statistical significance. The sum of these two coefficients' estimates is close to a unit, which is typical for GARCH models that are applied on the data of financial assets returns. This means that the shocks in the conditional variance equation will be long lasting. The great value of the sum of these two coefficients shows that the high rates of positive or negative returns leads to a large forecasted value of the variance in the prolonged period. The asymmetrical EGARCH (1,1) model has showed the best results in modeling the euro exchange rate returns. The asymmetry term in the conditional variance equation of this model is negative and statistically significant. A negative value of this term suggests that the positive shock has less impact on the conditional variance than the negative shocks. The asymmetric EGARCH (1,1) model provides evidence of a leverage effect.