Abstract
New functions are proposed for time series characterization based on a relationship between the Poisson integral and spectral analysis. These functions are shown to completely specify the correlation structure of a time series and can be estimated consistently and uniformly even if the time series has a mixed spectrum. They are also shown to be equipped with flexible parameters that can be used to achieve desired frequency selectability. Using these characterization functions, a new divergence measure is proposed for time series discrimination and change detection. Sensitivity of the new divergence is investigated under the additive and multiplicative spectral departure models. The divergence is shown to be more robust than some spectral-density-based divergence measures in fighting against narrow-band spectral contamination and distortion. A change-detection example in speech processing is given to demonstrate the effectiveness of the new method.