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Journal of Probability and Statistics
Volume 2012 (2012), Article ID 738636, 15 pages
http://dx.doi.org/10.1155/2012/738636
Research Article

G-Filtering Nonstationary Time Series

1Biostatistics Branch, NIH/NIEHS (National Institutes of Health/National Institute of Environmental Health Sciences), Research Triangle Park, NC 27709, USA
2Department of Mathematics, Odessa College, Odessa, TX 79764, USA
3Department of Statistical Science, Southern Methodist University, Dallas, TX 75205, USA

Received 16 August 2011; Revised 15 November 2011; Accepted 15 November 2011

Academic Editor: Shein-chung Chow

Copyright © 2012 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.

Abstract

The classical linear filter can successfully filter the components from a time series for which the frequency content does not change with time, and those nonstationary time series with time-varying frequency (TVF) components that do not overlap. However, for many types of nonstationary time series, the TVF components often overlap in time. In such a situation, the classical linear filtering method fails to extract components from the original process. In this paper, we introduce and theoretically develop the G-filter based on a time-deformation technique. Simulation examples and a real bat echolocation example illustrate that the G-filter can successfully filter a G-stationary process whose TVF components overlap with time.