Special half-day workshop on Wavelet Methods for Times Series Analysis Models

Abstract:

Course description: Wavelets have played a prominent role in the statistical analysis of time series since their introduction in the 1980s. This half-day workshop on wavelets will consist of two parts, each an hour and 45 minutes long. The first part will be a basic introduction to the key ideas behind the discrete wavelet transform (DWT), with emphasis on its physical interpretation and on two basic descriptors that arise from the DWT (an additive decomposition known as a multiresolution analysis, and an analysis of variance known as the wavelet variance or spectrum). The second part will expand upon these key ideas by looking at the interplay between the DWT and the statistical analysis of time series. In particular, the statistical theory behind wavelet variance analysis of intrinsically stationary processes will be reviewed, as will the extraction of signals buried in noise using a methodology known as wavelet shrinkage. The second part will conclude with a discussion of the DWT as a decorrelating transform for certain time series, leading to approximate maximum likelihood estimators for long-memory processes, fast simulation of time series, a test for homogeneity of variance, a test for trends in time series and a wavelet-based procedure for bootstrapping certain time-series statistics.

About the speaker: Don Percival is a Principal Mathematician at the Applied Physics Laboratory and a Professor in the Department of Statistics, University of Washington, Seattle, Washington. He is currently a visiting scientist at the Mathematics, Informatics and Statistics (CMIS) Division of CSIRO in Brisbane. He did his undergraduate work at the University of Pennsylvania (astronomy) and then pursued a masters degree at George Washington University (mathematical statistics) and a doctorate from the University of Washington (statistics), where he was the first doctoral student to graduate from the newly formed Department of Statistics. From 1968 to 1978 he was an Astronomer at the U.S. Naval Observatory in Washington, D.C., where he worked on the generation of atomic clock time scales and on the analysis of the frequency stability of high-performance oscillators. Dr. Percival’s research interests include spectral analysis, wavelets and use of statistical methodology in the physical sciences. He is the co-author (with Andrew Walden) of the textbooks Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques (1993) andWavelet Methods for Time Series Analysis (2000), both published by Cambridge University Press, Cambridge, England.