Applications of the TES modeling methodology

Abstract

TES (Transform-Expand-Sample)is a versatile methodology for modeling general stationary time series, and particularly those that are autocorrelated. The salient feature of TES lies in its ability to simultaneously capture firstorder and second-order properties of empirical time series ; given a sample data sequence, TES is designed to simultaneously capture any arbitrary marginal distribution and approximate the leading autocorrelations. Practical TES modeling is computationally intensive and can be effectively carried out only with software support. A computerized modeling environment, TEStool, has been designed to support the TES modeling methodology, through an interactive heuristic search approach facilitated by stateof-the-art data visualization techniques. The purpose of this paper is to present four examples of the effective use of the TES methodology to model various types of time series that arise in a variety of disciplines, ranging from manufacturing to financial modeling, with particular emphasis on video compression. These examples serve to highlight the efficacy and versatility of the TES modeling methodology.