Statistical distributions of time series in the frequency domain and the patterns of violation of white noise conditions

This paper investigates the distinction between white noise processes and their non-white noise counterparts in the frequency domain. It further examines the associated features and patterns for the process where white noise conditions are violated. The approach is then applied to US producer price index to illustrate the application. It is demonstrated that US PPI clearly possesses the features of a time series with the compounding effect.