Journal of Probability and Statistics
Volume 2013 (2013), Article ID 569597, 15 pages
Research Article

Using Time Deformation to Filter Nonstationary Time Series with Multiple Time-Frequency Structures

1Statistics Genomics Unit, NIH/NIMH (National Institutes of Health/National Institute of Mental Health), Bethesda, MD 20892, USA
2Department of Statistical Science, Southern Methodist University, Dallas, TX 75205, USA

Received 13 August 2012; Accepted 6 February 2013

Academic Editor: Zhidong Bai

Copyright © 2013 Mengyuan Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For nonstationary time series consisting of multiple time-varying frequency (TVF) components where the frequency of components overlaps in time, classical linear filters fail to extract components. The G-filter based on time deformation has been developed to extract components of multicomponent G-stationary processes. In this paper, we explore the wide application of the G-filter for filtering different types of nonstationary processes with multiple time-frequency structure. Simulation examples illustrate that the G-filter can be applied to filter a broad range of multicomponent nonstationary process where TVF components may in fact overlap in time.