Modeling Volatility in the Gambian Exchange Rate Returns Using Variants of ARMA–GARCH Models

Abstract

This thesis aimed at modeling exchange rate volatility in the Gambian foreign exchange rate returns. Financial time series models that combined autoregressive moving average and generalized conditional heteroscedasticity were explored theoretically and applied to the exchange rate returns of the Gambian Dalasi (GMD) against the Euro and United States dollars (USD). The data covers the period from January 2003 through January 2013 and represents daily spot exchange rates.. The properties of the daily Gambian exchange rate and returns data were examined and the best fitting autoregressive moving average and generalized conditional heteroscedasticity was selected after various model building stages namely, identification, estimation and how well the model captures the variation in the data have been critically evaluated. The autoregressive moving average process is used to model the mean equation and the residuals were fitted with a generalized conditional heteroscedasticity model. The autoregressive moving average process as the mean equation serves as a filter in order to remove serial dependence in the returns and to produce independent and identically distributed residuals.. The goodness of fit of the models were assessed by the Aikaike Information Criteria . Based on the Aikaike Information Criteria , the autoregressive moving average of order (1,1) with generalized conditional heteroscedasticity of order (1,1) and the autoregressive moving average of order (2,1) with the generalized conditional heteroscedasticity of order (1,1) were judged to be the best to model the mean equation and residuals of the GMD/Euro and GMD/USD return series. To check for leverage effects in the Gambian exchange rate market, the autoregressive moving average of order (1,1) with assymetric power autoregressive conditional heteroscedasticity of order (1,1) and the autoregressive moving average of order (2,1) with assymetric power autoregressive conditional heteroscedasticity of order (1,1) were included and fitted to the GMD/Euro and GMD/USD return series respectively. The empirical results revealed that the distribution of the return series was heavy-tailed and volatility was highly persistent in the Gambian foreign exchange market. Using the two models for each exchange rate returns, 150 out-of-sample forecast of volatility– measured as the conditional variance– were generated. The mean absolute error and the root mean square error were used to assess the forecast accuracy. Based on these metrics in assessing the out-of-sample forecast, the autoregressive moving average of order (1,1) with generalized conditional heteroscedasticity of order (1,1) slightly perform better than the the autoregressive moving average of order (1,1) with assymetric power autoregressive conditional heteroscedasticity of order (1,1) for the GMD/Euro whilst the autoregressive moving average of order (2,1) with the generalized conditional heteroscedasticity of order (1,1) forecasted the volatility better than theautoregressive moving average of order (2,1) with assymetric power autoregressive conditional heteroscedasticity of order (1,1) in the GMD/USD returns. The Diebold- Mariano test of forecast accuracy was performed on the two models applied to each currency to establish which model is superior in forecasting volatility . However, the results shows that the two models applied to each currency have the forecasting accuracy.