The purpose of this study describes financial time series modelling with special application to modelling inflation data for Kenya. Specifically the theory of time series is modelled and applied to the inflation data spanning from January 1985 to April 2016 obtained from the Kenya National Bureau of Statistics. The arch type family models were fitted and forecast to the data because data was characterized by variation in variance and mean. The outcome of the study revealed that the ARCH –family type models, particularly, the EGARCH (1, 1) with generalized error distribution (GED) was the best in modelling and forecasting Kenya’s monthly rates of inflation. The study recommends that governments, policy makers interested in modelling and forecasting monthly rates of inflation should take into consideration Heteroscedastic models since it captures the volatilities in the monthly rates of inflation.