The inflation rate in Nigeria has persistence, nonlinear exchange-rate effects, and large seasonal variations, making the forecasting of Nigeria’s inflation rate hard using standard linear time series models. Models of this type usually capture only one of the features and produce unstable forecasts and, importantly for developing economies, the impact of the exchange rate on inflation rate. A Fourier-Polynomial Time Series Regression (FP-TSR) model is proposed, which incorporates autoregressive dynamics, polynomial nonlinearity, interaction effects and Fourier components into a single framework. We analysed the monthly inflation and exchange rate data from the World Bank January 2004 to December 2024. Model parameters were estimated using ordinary least squares. Model fit was evaluated using the coefficient of determination ($R^2$) and adjusted $R^2$, while forecasting performance was assessed using root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The results reveal strong inflation persistence and statistically significant nonlinear exchange-rate effects. The FP-TSR model achieves an $R^2$ of 0.933. In forecasting performance, it reduces RMSE, MAE, and MAPE by 1.41\%, 3.06\%, and 3.40\%, respectively, relative to the lagged regression model. These findings demonstrate consistent improvement in both explanatory power and predictive accuracy compared to polynomial, Fourier-only, and lagged regression models. The proposed model significantly improves inflation forecasting performance and provides a robust, policy-relevant tool for short-term inflation forecasting in Nigeria and offers a flexible structure for modelling macroeconomic time series exhibiting similar variation.