TIME SERIES ANALYSIS OF EXCHANGE RATES: A MODEL COMPARATIVE STUDY
Abstract
This study presents a comparative time series analysis of the Nigerian exchange rate
using ARIMA and GARCH models to investigate trend behavior and volatility dynamics.
Monthly USD/NGN exchange rate data spanning from January 2004 to December 2021
(216 observations) were analyzed. The Augmented Dickey-Fuller (ADF) test was employed to test for stationarity, and transformations were applied where necessary. ARIMA models were developed using the Box-Jenkins methodology, while the GARCH model captured time-varying volatility. Results showed that the exchange rate series is non-stationary at level but stationary after first differencing, suggesting it is integrated of order one, I(1). The MA(1) model was identified as the best ARIMA specification. The GARCH(1,2) model effectively captured volatility clustering, although residual heteroskedasticity remained. Performance comparison using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) revealed that ARIMA provided stable forecasts, while GARCH excelled in volatility representation. The study concludes that no single model suffices for all objectives. ARIMA is suitable for trend forecasting, while GARCH is ideal for volatility analysis. Future research could explore hybrid ARIMA-GARCH models and include exogenous variables through ARIMAX frameworks. Keywords: Exchange rate, Time series, ARIMA, GARCH, Forecasting, Nigeria, Volatility
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