Forecasting the Naira–Pound Sterling Exchange Rate: A Comparative Analysis of ARIMA, ARIMAX and ARIMA-GARCH Models
Accurate exchange-rate forecasting is important for financial planning, international trade, investment decisions and macroeconomic management. This study develops and compares three time-series forecasting approaches for the Naira–Pound Sterling exchange rate: autoregressive integrated moving average (ARIMA), autoregressive integrated moving average with exogenous variables (ARIMAX), and ARIMA combined with generalized autoregressive conditional heteroskedasticity (ARIMA-GARCH). A synthetic monthly dataset comprising 180 observations from January 2008 to December 2022 was generated specifically for methodological and forecasting-model evaluation. The synthetic observations are not presented as official historical observations. The analysis uses ARIMA(1,1,1) as the benchmark model, while ARIMAX incorporates the interest-rate differential, inflation differential, crude-oil price and Nigerian foreign-exchange reserves. ARIMA-GARCH combines an ARIMA conditional-mean specification with a GARCH(1,1) conditional-variance specification. The first 144 observations were used for model estimation and the final 36 observations were reserved for out-of-sample forecasting. Forecasting accuracy was evaluated using mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE). The simulated results show that ARIMAX achieved the lowest RMSE of 7.3931, while ARIMA recorded the lowest MAE and MAPE of 6.6043 and 3.4729%, respectively. ARIMA-GARCH produced results very close to the ARIMA benchmark.