Modelling the CPI using a lognormal diffusion process and implications on forecasting inflation

The Maximum Likelihood estimator is used within a lognormaldiffusion process and closed form analytical solutions are obtained.The monthly CPI forecasts are estimated for the period between1970 and 2002. The quarterly estimates of inflation rates areobtained from monthly forecasts rather than from quarterly data.This has significantly improved the estimates of inflation rates.The model also produced a superior fit as compared to randomwalk and GARCH(p,q)-M models. The adopted approach is foundto be simple, economical and generally suitable for modellingstochastic processes that reflect aggregation over time stemmingfrom many factors, and in which the transition path betweenconsecutive states is relatively smooth.