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.
Timinibife N. Charles, T. I. AyakemeKtrend - International Journal of Mathematics and Statistics (IJMS) · 2026
This study presents a stochastic SEIARV model for analysing COVID-19 transmission and vaccination intervention. The model incorporates symptomatic and asymptomatic infectious individuals, demographic recruitment and mortality, disease-induced mortality, incomplete vaccine protection, and stochastic fluctuations in epidemic dynamics. The basic reproduction number, $R_0$, is derived using the next-generation matrix approach, and the disease-free and endemic equilibria are analysed. The stochastic model is solved numerically using the Euler--Maruyama method, and multiple sample paths are generated to examine uncertainty in epidemic trajectories. Numerical results show that vaccination reduces both the reproduction number and the peak infectious population. In particular, increasing the vaccination rate from the baseline level to five times its value reduces $R_0$ below unity and substantially decreases the epidemic peak. The results demonstrate the importance of vaccination in reducing COVID-19 transmission and highlight the value of stochastic modelling in capturing variability and uncertainty in epidemic outcomes.
Aniayam B. Okrinya, Timinibife N. CharlesKtrend – Nigerian Journal of Mathematical and Computational Sciences · 2026
The recovery of biological parameters from fractional HIV trajectories is examined alongside the mathematical properties of hybrid neural activations. Using the model of Okeke et al. [1] and the five-component activation mixture of Essang et al. [2], an exact parameter symmetry is derived: proliferation rate, healthy-cell death rate and carrying capacity cannot all be recovered separately from the model trajectories without additional information. A reduced parametrisation eliminates this redundancy. Conditional identifiability of the reduced coefficients is established through full-rank trajectory regressors for a known fractional order and fully observed states. The hybrid activation derivative is corrected, and global scalar slope bounds are proved. These bounds do not guarantee preservation of gradients through arbitrary network depth. A fractional residual learning framework is specified, and completed synthetic experiments examine parameter symmetry, regressor singular values, observation-window conditioning and slope products. The study establishes mathematical and computational limitations rather than empirical superiority of a trained learning algorithm.
Okeke Ikenna StephenKtrend – Nigerian Journal of Mathematical and Computational Sciences · 2026
