Time series of monthly and yearly inflation rates and their properties

Monthly and yearly inflation rates can be understood as rates of dynamics of the basic inflation indicator i.e. the consumer price index. These indicators modify the original inflation information. It is important to analyze the difference of the consumer price index, monthly and yearly inflation rates, from the viewpoint of their frequency content, time lag and deformations. The theory of linear filtration and its representation in the frequency domain is used. Under particular assumptions, in the time series of yearly inflation rate there can be spurious cycles and high-frequency motions. The time series of yearly inflation rate lags behind the time series of instantaneous inflation rate about six months in low frequencies and the time series of monthly inflation rate lags behind the time series of instantaneous inflation rate about half of the month in all frequencies.