LOCAL SPECTRAL ENVELOPE: AN APPROACH USING DYADIC TREE-BASED ADAPTIVE SEGMENTATION

DAVID S. STOFFER^{1} , HERNANDO C. OMBAO^{2} AND DAVID E. TYLER^{3}

1Department of Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A. 2Department of Statistics and Department of Psychiatry, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A. 3Department of Statistics, Rutgers University, New Brunswick, NJ 08903, U.S.A.

(Received February 19, 2001; revised July 22, 2001)

Abstract. The concept of the spectral envelope was introduced as a statistical basis for the frequency domain analysis and scaling of qualitative-valued time series. A major focus of this research was the analysis of DNA sequences. A common problem in analyzing long DNA sequence data is to identify coding sequences that are dispersed throughout the DNA and separated by regions of noncoding. Even within short subsequences of DNA, one encounters local behavior. To address this problem of local behavior in categoricalvalued time series, we explore using the spectral envelope in conjunction with a dyadic tree-based adaptive segmentation method for analyzing piecewise stationary processes.

Key words and phrases: DNA sequences, gene detection, spectral envelope, dyadictree based methods, adaptive segmentation, categorical-valued time series, timevarying spectrum, optimal scaling, Fourier analysis, signal detection.