Time-Varying Parameter Forecasting of Nigeria's Inflation: A Comparative Evaluation of GARCH-Family Models and the Kalman Filter

Abstract

Reliable Inflation forecasts serve as the basic component for designing sound financial and monetary policy and implementing useful financial plan. They are needed for macro-financial stability even more so in the emerging countries where structural reform and external disturbance tends to change inflation dynamics on and over time. This study compared performance of GARCH-family models against time-varying state-space Kalman filter in time varying parameters framework using monthly inflation data of Nigeria during the periods January 2000 – December 2025. The models included GARCH(1,1), EGARCH(1,1), TGARCH(1,1), APARCH(1,1), Kalman filter through time-varying coefficients state-space model. Diagnostic statistics are examined to check adequate fit while RMSE, MAE, MAPE, Theil's U statistics and directional Accuracy criteria are used to evaluate forecast performance for in sample and out of sample estimates. The empirical results showed the inflation processes in Nigeria are generally persistent and characterized by volatilities in clusters and asymmetric response to shocks. APARCH(1,1) performs better among GARCH-family models from both statistical fitting and forecasting performance. Nevertheless, all Kalman filter approach performs best in term of performance measured by highest likelihood estimate, lowest information criteria and lowest forecast errors (RMSE=0.517, MAE=0.408, MAPE =6.29%, Theil's U = 0.286) with highest directional accuracy 84.1 percent out of sample among all competing models. This results indicated dynamic state space model captures dynamic inflation better than fixed parameters-volatility models. And Kalman filter model can give much better guidance for forecasting on the Nigerian inflation. Hence we can employ Kalman filter in designing financial planning and executing monetary policy.