The paper aimed at modelling the density of inflation based on time-varying conditional variance, skewness and kurtosis model developed by Leon, Rubio, and Serna (2005) who model higher-order moments as GARCH-type processes by applying a Gram-Charlier series expansion of the normal density function. Additionally, it extended their work by allowing both conditional skewness and kurtosis to have an asymmetry term. The results revealed the significant persistence in conditional variance, skewness and kurtosis which indicate high asymmetry of inflation. Additionally, diagnostic tests reveal that models with nonconstant volatility, skewness and kurtosis are superior to models that keep them invariant.