Bispectral-Based Methods for Clustering Nonlinear Time Series

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Bonnie K. Ray*+ and Jane Harvill and Nalini Ravishanker
• Companies: IBM Thomas J. Watson Research Center and Baylor University and University of Connecticut
• Keywords: nonlinear ; clustering ; frequency domain ; bispectrum

Abstract

It is well-known that in general, second-order properties are insufficient for characterizing nonlinear time series. In particular, the normalized bispectral density function is constant for a linear, Gaussian series, but typically not for nonlinear series. Furthermore, different nonlinear time series models have different bispectral signatures. Based on these properties, we propose the use of distance measures based on the squared modulus of the estimated normalized bispectrum as a means for clustering nonlinear series. In this talk, we summarize the performance of agglomerative clustering methods that use distance measures computed from the estimated bispectrum for a mix of linear and nonlinear time series. We then present an application of the methods to a set of gamma-ray burst time profiles, to aid astrophysicists in identifying sets of gamma-ray bursts emanating from the same type of astral event.