Read more
Zusatztext "...an interested reader should be able to acquire a decent grounding in the subject area covered." (International Statistical Review! 2007) Informationen zum Autor Wilfredo Palma , PhD, is Chairman and Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. Dr. Palma has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics. Klappentext A self-contained, contemporary treatment of the analysis of long-range dependent dataLong-Memory Time Series: Theory and Methods provides an overview of the theory and methods developed to deal with long-range dependent data and describes the applications of these methodologies to real-life time series. Systematically organized, it begins with the foundational essentials, proceeds to the analysis of methodological aspects (Estimation Methods, Asymptotic Theory, Heteroskedastic Models, Transformations, Bayesian Methods, and Prediction), and then extends these techniques to more complex data structures.To facilitate understanding, the book:*Assumes a basic knowledge of calculus and linear algebra and explains the more advanced statistical and mathematical concepts*Features numerous examples that accelerate understanding and illustrate various consequences of the theoretical results*Proves all theoretical results (theorems, lemmas, corollaries, etc.) or refers readers to resources with further demonstration*Includes detailed analyses of computational aspects related to the implementation of the methodologies described, including algorithm efficiency, arithmetic complexity, CPU times, and more*Includes proposed problems at the end of each chapter to help readers solidify their understanding and practice their skillsA valuable real-world reference for researchers and practitioners in time series analysis, economerics, finance, and related fields, this book is also excellent for a beginning graduate-level course in long-memory processes or as a supplemental textbook for those studying advanced statistics, mathematics, economics, finance, engineering, or physics. A companion Web site is available for readers to access the S-Plus(r) and R data sets used within the text. Zusammenfassung During the last decades long-memory processes have evolved as a vital and important part of time series analysis. This book attempts to give an overview of the theory and methods developed to deal with long-range dependent data as well as describe some applications of these methodologies to real-life time series. Inhaltsverzeichnis Preface xiii Acronyms xvii 1 Stationary Precedes 1 1.1 Fundamental concepts 2 1.1.1 Stationarity 4 1.1.2 Singularity and Regularity 5 1.1.3 Wold Decomposition Theorem 5 1.1.4 Causality 7 1.1.5 Invertibility 7 1.1.6 Best Linear Predictor 8 1.1.7 Szego-Kolmogorov Formula 8 1.1.8 Ergodicity 9 1.1.9 Martingales 11 1.1.10 Cumulants 12 1.1.11 Fractional Brownian Motion 12 1.1.12 Wavelets 14 1.2 Bibliographic Notes 15 Problems 16 2 State Space Systems 21 2.1 Introduction 22 2.1.1 Stability 22 2.1.2 Hankel Operator 22 2.1.3 Observability 23 2.1.4 Controllability 23 2.1.5 Minimality 24 2.2 Representations of Linear Processes 24 2.2.1 State Space Form to Wold Decomposition 24 2.2.2 Wold Decomposition to State Form 25 2.2.3 Hankel Operator to State Space Form 25 2.3 Estimation of the State 26 2.3.1 State Predictor 27 2.3.2 State Filter 27 2.3.3 State Smoother 27 2.3.4 Missing Observation 28 2.3.5 Steady State System 28 2.3.6 Prediction of Future O...
List of contents
Preface.
Acronyms.
1. Stationary Processes.
2. State Space Systems.
3. Long-Memory Processes.
4. Estimation Methods.
5. Asymptotic Theory.
6. Heteroskedastic Models.
7. Transformations.
8. Bayesian Methods.
9. Prediction.
10. Regression.
11. Missing Data.
12. Seasonality.
References.
Topic Index.
Author Index.
Report
"...Palma presents a textbook for a graduate course summarizing the theory and methods developed to deal with long-range-dependent data, and describing some applications to real-life time series." (SciTech Book Reviews, June 2007)
"...textbook for a graduate course summarizing the theory and methods developed to deal with long-range-dependent data, and describing some applications to real-life time series.... Problems and bibliographic notes are provided at the end of each chapter." (SciTech Book News, June 2007)
"I believe that this text provides an important contribution to the long-memory time series literature. I feel that it largely achieves its aims and could be useful for those instructors wishing to teach a semester-long special topics course.... I strongly recommend this book to anyone interested in long-memory time series. Both researchers and beginners alike will find this text extremely useful." (Journal of the American Statisticial Association, Dec 2008)
"Very well-organized catalogue of long-memory time series analysis." (Mathematical Reviews, 2008)
"Judging by its contents and scope [the aim of this book] has been largely achieved.... The list of references is selective but quite comprehensive. Each chapter concludes with a 'Problems' section which should be helpful to instructors wishing to use this book as standalone basis for a course in its subject area..." (International Statistical Review, 2007)
