Signal extraction. Efficient estimation, `unit root'-tests and early detection of turning points.
type: Item
instance of: scholarly article
title: Signal extraction. Efficient estimation, `unit root'-tests and early detection of turning points.
zbMATH Open document ID: 1053.93003
author: Marc Wildi
published in: Lecture Notes in Economics and Mathematical Systems
publication date: 2004-11-29T00:00:00Z
review text: A new method, called Direct Filter Approach (DFA), is presented in the book. It is intended to solve the well-known signal estimation problem, related with the fast detection of turning-points in time series. Often, signal estimates are subject to significant time delays towards the end point of a finite sample. Therefore, turning-points of the signal cannot be detected in time. The DFA proposed in the book enables one to constrain filters such that the time delay becomes smaller. These issues are studied in the book. The book is organized as follows: Chapter 1 provides an overview on the problem. A brief description of the well-known Model Based Approach (MBA) is given. It is shown that it may be inefficient in the context of fast detection of turning-points in time series. The need of an efficient general signal estimation method for these important applications is demonstrated. In chapter 2, MBAs are presented. The objective is to compare the proposed DFA with established MBAs, and to use two of most popular MBAs as ``benchmarks'' in chapters 7 and 8. The aim of the author is not to provide an exhaustive list of existing methods but to describe established procedures which are implemented in ``widely used'' software packages. In chapter 3 the main concepts are proposed that are needed for the description of filters in the frequency domain (such as transfer functions, amplitude functions or phase functions). A new class of Zero-Pole-Combination (ZPC) filters is derived. Their characteristics ``match'' the signal estimation problem. In chapter 4 properties of the periodogram and technical details related to the DFA are analyzed. For the DFA, an eminent role is awarded to the periodogram (or to statistics directly related to the periodogram). It ``collects'' and transforms the information of the sample \(X_1,\dots, X_N\) into a form suitable for the signal estimation problem. In particular, the statistic is analyzed for integrated processes. Stochastic properties of…
Mathematics Subject Classification ID: 93-02
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 94A13
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 93E12
Mathematics Subject Classification ID: 94-02
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 2120170
zbMATH Keywords: system identification
zbMATH Keywords: estimation and detection
zbMATH Keywords: detection theory
zbMATH Keywords: sampled data systems
reviewed by: Tzvetan Semerdjiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2120170