Discrimination of Time Series by Parametric Filtering
Abstract A new approach to time series discrimination is discussed. The approach, called parametric filtering, combines a parametric filter bank with an analysis of first-order autocorrelation from the filtered time series. As a function of the filter parameter, the first-order autocorrelation is shown to uniquely characterize the correlation structure of the original stationary time series. It is also shown to produce a diagnostic that not only characterizes correlation structures, but also transforms these structures into smooth and monotone functions. Natural sample estimators of these characterization functions are shown to be uniformly consistent even for mixed-spectrum time series. Examples are provided to demonstrate the potential applications of the method in discrimination of time series with a special emphasis on time series of mixed spectra.