Development of Statistical Models for Predicting Nigeria’s GDP Rate for Economic Growth

Accurate forecasting of Gross Domestic Product (GDP) growth is essential for effective economic planning, policy formulation, and sustainable development. This study developed and compared the forecasting performance of Autoregressive Integrated Moving Average (ARIMA) and Fourier time series models for predicting Nigeria's quarterly GDP growth rate. Quarterly GDP growth data covering the period from 2010Q1 to 2025Q4 obtained from the National Bureau of Statistics (NBS) were analyzed using R statistical software. The statistical properties of the series were examined using descriptive statistics, time series plots, the Autocorrelation Function (ACF), and Partial Autocorrelation Function (PACF). Stationarity was assessed using the Augmented Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests, which indicated that the original series was non-stationary but became stationary after first differencing. Ten ARIMA models and ten Fourier model specifications were estimated and compared using the Akaike Information Criterion (AIC). The ARIMA(1,1,1) model emerged as the best ARIMA model with the lowest AIC, while the Linear Trend + 1 Harmonic model was selected as the best Fourier model. Model adequacy was evaluated using the Ljung–Box and ARCH-LM diagnostic tests. Forecasting performance was assessed using the Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results showed that the ARIMA(1,1,1) model achieved lower forecast errors (RMSE = 0.0177, MAE = 0.0101) than the Linear Trend + 1 Harmonic Fourier model (RMSE = 0.0254, MAE = 0.0200), demonstrating superior forecasting accuracy. The study concludes that the ARIMA(1,1,1) model provides a more reliable framework for forecasting Nigeria's quarterly GDP growth than the Fourier model. The findings provide useful empirical evidence for policymakers, economists, and development planners seeking accurate GDP forecasts for macroeconomic planning and policy evaluation.