Macroeconmic datasets has been analysed with various techniques. Traditional econometric approaches failed to capture cyclical and periodic structures in macroeconomic data, resulting in weak forecasts. This study addresses this gap by applying a Time Series Fourier Regression (TSFR) model to evaluate the impact of exchange rate fluctuations on Nigeria’s economic growth. Annual data on Gross Domestic Product (GDP) and official exchange rates from 1960 to 2023 were obtained from the Central Bank of Nigeria (CBN). The TSFR model was estimated using the Ordinary Least Squares (OLS) method and validated through the Durbin-Watson (DW) statistic, residual histograms, and Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) checks. Model performance was benchmarked against multiple regression, lagged regression and multiple Fourier regression models using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). It was revealed that exchange rate fluctuations significantly influence GDP. The TSFR model explained over 80% of GDP variability, with an adjusted coefficient of determination (R-squared) of 78%. Diagnostic tests confirmed normally distributed residuals without serial correlation. Comparative analysis demonstrated that the TSFR model consistently outperformed alternative models in terms of explanatory power and forecast accuracy. The results gives reliable insights into the dynamics between exchange rates and economic growth.
The study establishes that Fourier-based time series models provide a superior framework for analysing macroeconomic data, effectively capturing both secular and cyclical movements.