Mathematical Modelling and Forecasting of Inflation Dynamics in Nigeria Using ARIMA, Prophet, and Markov Chain Models

This study develops and compares three mathematical frameworks for modelling monthly inflation dynamics in Nigeria: an autoregressive integrated moving-average model, a Prophet additive forecasting model, and a finite-state Markov chain. The analysis uses 281 monthly observations of headline inflation covering January 2003 to May 2026. Preliminary tests indicate that the level series is non-stationary, while first differencing produces a stationary process. A systematic information-criterion search selected an ARIMA(2,1,3) model. A twelve-month holdout experiment showed that ARIMA outperformed Prophet, with mean absolute error, root mean squared error, and mean absolute percentage error of 6.69, 7.60, and 41.08%, respectively, compared with 16.16, 16.92, and 95.39% for Prophet. The relatively large errors reflect a major structural discontinuity near the end of the sample and demonstrate the difficulty of extrapolating inflation under changing measurement and macroeconomic regimes. The Markov model classified inflation as low, moderate, or high and revealed strong state persistence, with self-transition probabilities of 0.913, 0.945, and 0.936. Its stationary distribution assigns probabilities of 0.246, 0.586, and 0.168 to the low, moderate, and high regimes. The combined evidence shows that ARIMA is more effective for short-run numerical forecasting, Prophet is useful for decomposable trend-seasonal representation but is vulnerable to abrupt breaks, and the Markov chain provides interpretable regime probabilities. The study recommends ensemble forecasting, explicit structural-break treatment, and periodic model re-estimation for policy-oriented inflation monitoring in Nigeria.