Analysis of Time Series Structure: SSA and Related Techniques, 1st Edition (Hardback) book cover

Analysis of Time Series Structure

SSA and Related Techniques, 1st Edition

By Nina Golyandina, Vladimir Nekrutkin, Anatoly A Zhigljavsky

Chapman and Hall/CRC

320 pages

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Hardback: 9781584881940
pub: 2001-01-23
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Description

Over the last 15 years, singular spectrum analysis (SSA) has proven very successful. It has already become a standard tool in climatic and meteorological time series analysis and well known in nonlinear physics and signal processing. However, despite the promise it holds for time series applications in other disciplines, SSA is not widely known among statisticians and econometrists, and although the basic SSA algorithm looks simple, understanding what it does and where its pitfalls lay is by no means simple.

Analysis of Time Series Structure: SSA and Related Techniques provides a careful, lucid description of its general theory and methodology. Part I introduces the basic concepts, and sets forth the main findings and results, then presents a detailed treatment of the methodology. After introducing the basic SSA algorithm, the authors explore forecasting and apply SSA ideas to change-point detection algorithms. Part II is devoted to the theory of SSA. Here the authors formulate and prove the statements of Part I. They address the singular value decomposition (SVD) of real matrices, time series of finite rank, and SVD of trajectory matrices.

Based on the authors' original work and filled with applications illustrated with real data sets, this book offers an outstanding opportunity to obtain a working knowledge of why, when, and how SSA works. It builds a strong foundation for successfully using the technique in applications ranging from mathematics and nonlinear physics to economics, biology, oceanology, social science, engineering, financial econometrics, and market research.

Reviews

"[This] is the first book on SSA aimed at statisticians. The authors provide clear and concise descriptions of the basic methodology of this new technique, and this is a welcome reference text for time series practitioners. … This book provides the background to successfully understand and intelligently apply SSA. I strongly recommend it to anyone interested in time series analysis."

- Journal of the American Statistical Association

"This book summarizes the results published on SSA in the last 15 years. It is a good source of SSA methodology for scientists who wish to complement classical procedures for time series analysis by SSA tools."

- Mathematical Reviews, Issue 2002

"…the formal mathematical theory, which underpins the method, is laid out with admirable clarity. The authors have performed a service to the statistical community by writing this book. It is likely to become the standard reference to SSA; helpful to the applied statistician who wishes to analyse a times series and also to the theoretician who may wish to develop this interesting approach to time series analysis further."

Short Book Reviews of the ISI

"The present monograph is dedicated to a recently proposed technique, singular spectrum analysis (SSA), that can be considered an extension of Pearson's problem to the situation in which the points in the space correspond to realizations of a time series…it is an important contribution to a modern area that is becoming increasingly needed in problems of electrical engineering, economics, meteorology, oceanography, and other fields. The authors should be commended for bringing this method to the attention of the statistical community."

-Andrew L. Rukhin, University of Maryland at Baltimore County for Technometrics, August 2002

Table of Contents

Preface

Notation

Introduction

PART I SSA: METHODOLOGY

BASIC SSA

Basic SSA: Description

Steps in Basic SSA: Comments

Basic SSA: Basic Capabilities

Time Series and SSA Tasks

Separability

Choice of SSA Parameters

Supplementary SSA techniques

SSA FORECASTING

SSA Recurrent Forecasting Algorithm

Continuation and Approximate Continuation

Modifications to Basic SSA R-Forecasting

Forecast Confidence Bounds

Summary and Recommendations

Examples and Effects

SSA DETECTION OF STRUCTURAL CHANGES

Main Definitions and Concepts

Homogeneity and Heterogeneity

Heterogeneity and Separabiity

Choice of Detection Parameters

Additional Detection Characteristics

Examples

PART II SSA: THEORY

SINGULAR VALUE DECOMPOSITION

Existence and Uniqueness

SVD Matrices

Optimality of SVDs

Centering in SVD

TIME SERIES OF FINITE RANK

Time Series Of Finite Rank

General Properties

Series of Finite Rank and Recurrent Formulae

Time Series Continuation

SVD OF TRAJECTORY MATRICES

Mathematics of Separability

Hankelization

Centering in SSA

SSA for Stationary Series

List of Data Sets and Their Sources

References

Index

About the Series

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

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Subject Categories

BISAC Subject Codes/Headings:
MAT029000
MATHEMATICS / Probability & Statistics / General