Stochastic Modelling and Long-Horizon Forecasting of Food Inflation in Nigeria

Abstract

Food inflation constitutes one of the most volatile and economically significant components of 
the consumer price index in developing economies, with profound implications for household 
welfare, food security, poverty levels, and macroeconomic stability. In Nigeria, persistent 
fluctuations in food prices have intensified concerns regarding the effectiveness of monetary 
and fiscal policy interventions aimed at maintaining price stability. This study applies 
stochastic time-series modeling techniques to analyze and forecast food inflation dynamics 
in Nigeria using monthly food inflation data spanning January 2004 to December 2023. The 
methodological framework is based on the Autoregressive Integrated Moving Average 
(ARIMA) model, following rigorous statistical procedures including stationarity testing, 
differencing, model identification, parameter estimation, and diagnostic evaluation. The 
results indicate that the food inflation series exhibits non-stationary behavior at level but 
achieves stationarity after first differencing. Among the competing specifications examined, 
the ARIMA(1,1,1) model emerged as the most parsimonious and statistically robust 
forecasting model based on established information criteria and residual diagnostic tests. 
Empirical findings reveal strong inflation persistence, suggesting that past food price shocks 
continue to influence future inflationary movements. Furthermore, the observed volatility 
clustering indicates periods of heightened inflation uncertainty followed by relatively tranquil 
phases, reflecting the inherent instability of food price dynamics in Nigeria. Long-term 
forecasts generated from the fitted ARIMA (1,1,1) model over 5-, 10-, and 20-year horizons 
project sustained upward pressure on food prices, accompanied by widening forecast intervals 
that signify increasing uncertainty over time. The study provides a mathematical and empirical 
justification for ARIMA-based forecasting of food inflation and contributes to the growing 
literature on inflation modeling, forecasting, and policy analysis in developing African 
economies.