Modified Geometric Brownian Motion For Inflation Modelling

Accurate inflation forecasting is vital for effective economic planning, monetary policy formulation, and investment decisionmaking, especially in developing economies like Nigeria. Traditional models such as ARIMA and standard Geometric Brownian Motion (GBM) often assume constant parameters and may fail to capture the dynamic and volatile nature of inflation. This study introduces a novel Dynamic Geometric Brownian Motion (DGBM) model that incorporates rolling window estimates of drift and volatility to account for structural changes and macroeconomic shocks over time. Monthly inflation rate data from January 2003 to December 2024, obtained from the Central Bank of Nigeria, was used to compare the forecasting performance of three models: ARIMA, Traditional GBM, and the proposed Dynamic GBM. Model accuracy was evaluated using metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and R-squared (R²). Diagnostic tests including the Augmented Dickey-Fuller, Shapiro-Wilk, and Ljung-Box were conducted to validate model assumptions. The results revealed that while the traditional GBM model performed poorly due to its rigid assumptions, the Dynamic GBM significantly outperformed both ARIMA and standard GBM models in terms of forecast accuracy and adaptability. The DGBM model achieved an R² of 0.966, demonstrating its strong predictive power. The study recommends the integration of the Dynamic GBM model into macroeconomic forecasting tools for more responsive and reliable inflation prediction.