Modelling the consumer price index using a lognormal diffusion process and implications on forecasting inflation

The Maximum Likelihood estimator is used within a lognormal diffusion process and closed form analytical solutions are obtained. The monthly CPI forecasts are estimated for the period between 1970 and 2002. The quarterly estimates of inflation rates are obtained 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 random walk and GARCH(p,q)–M models. The adopted approach is found to be simple, economical and generally suitable for modelling stochastic processes that reflect aggregation over time stemming from many factors, and in which the transition path between consecutive states is relatively smooth.