Application of Fourier Series in Analysing Seasonal Patterns in Nigerian Agricultural Commodity Prices

Seasonal price volatility in agricultural commodity markets poses significant welfare risks for smallholder farmers and urban food consumers across Nigeria. This study applies Fourier series decomposition to identify and characterise cyclical seasonal patterns in monthly retail prices of maize, rice, and tomatoes across markets in six geopolitical zones over the period 2018 to 2023. Price data are sourced from the National Bureau of Statistics Food Price Watch reports and the National Agricultural Extension and Research Liaison Services commodity monitoring database. The Fourier series representation decomposes each commodity's price time series into harmonic components, with the dominant periodicity, amplitude, and phase angle estimated using ordinary least squares regression on trigonometric regressors. Results confirm statistically significant biannual price cycles in maize and rice, with price peaks coinciding with the pre-harvest lean seasons of February to March and September to October. Tomato prices exhibit more irregular cycles with dominant periodicity of approximately four months, reflecting shorter production cycles and high perishability. The Fourier models achieve R-squared values exceeding 0.71 for all three commodities when seasonal harmonics are combined with trend components. The study recommends that the Federal Ministry of Agriculture publish Fourier-based seasonal price forecasts quarterly to inform farmer planting decisions and trader stocking behaviour. Keywords: Fourier series, seasonal price patterns, agricultural commodities, Nigerian markets, price decomposition.