Modeling with ARIMA-ARCH/GARCH Techniques to Estimate Weekly Exchange Rate of Liberia

Abstract

The current research employs the estimations of univariate linear time series, ARIMA and two traditional volatility time series models, ARCH and GARCH to analyze the behavior of exchange rate volatility in the Liberian economy using weekly time series observation spanning from January 07, 2013 to December 25, 2017. This study estimated the parameters of the selected models and detected the irregular pattern the financial series portrays in the Liberian economy. Evidently, the paper finds huge volatility and fat tail distribution in the exchange rate series of Liberia and as such the series behavior is worrisome which needs to be expediently modeled well. Additionally, the ARCH and GARCH models were estimated separately to capture the volatility pattern in the series. The results show that there is persistence volatility in the financial series as the estimated ARCH parameter was equal to unity and the sum of the ARCH and GARCH terms were close to unity in the GARCH(1,1) specification. On the other hand, after assuming generalized error distribution for the exchange rate series due to its fat tail, the parameters on the volatility models reduced significantly but the means of these equations were practically zero. In addition, the two volatility models were re-estimated to the residuals of the ARIMA to model the noise in the univariate time series model. The results reveal that the models performed remarkably well when fitted to the residuals of the ARIMA(1,1,2) model. The recommendation from this empirical research is that with the high persistence in the series and the risk as well as the very low returns it comes with, modelers and policymakers should estimate the parameters of the exchange rate effectively and with care before any point forecast can come into play because knowledge about the distribution and the calculated returns will all aid in better prediction.

Keywords: Exchange rate volatility, ARIMA model, ARCH model, GARCH model, Volatility clustering, Liberia