Asian Journal of Probability and Statistics

This study models daily USD/NGN exchange-rate volatility using an autoregressive moving-average–generalised autoregressive conditional heteroskedasticity (ARMA–GARCH) framework. The analytical series covers December 2024 through July 2026. The imported file contained 403 rows; duplicate-date screening yielded 397 unique exchange-rate observations and 396 percentage log returns. The Augmented Dickey–Fuller test rejected a unit root in the return series (test statistic = −8.6721, p < .001), while ARCH–LM tests at lags 5, 10 and 15 detected conditional heteroskedasticity (all p < .001). Among the reported low-order ARMA candidates, ARMA(2,2) was retained because it was the only specification with a Ljung–Box Q(10) p-value above .05, despite not minimising the information criteria. The reported Gaussian ARMA(2,2)–GARCH(1,1) fit produced ARCH and GARCH estimates of α = 0.366944 and β = 0.316000, giving α + β = 0.682944. This value is below unity and therefore indicates a finite-variance, mean-reverting conditional-volatility process under the fitted specification. Post-estimation ARCH–LM tests did not detect remaining ARCH effects at the examined lags. Point volatility forecasts increased from 0.3598% at one trading day ahead to 0.5058% at ten trading days ahead and approached the model-implied long-run daily volatility of approximately 0.5100% over a 30-trading-day horizon. The findings support the presence of time-varying but mean-reverting USD/NGN volatility during the study window. Because the analysis does not include an out-of-sample forecast-accuracy exercise or coefficient-level inferential statistics, the conclusions are limited to the reported sample, diagnostics and point forecasts.