Modern Spectrum Analysis of Time Series

Fast Algorithms and Error Control Techniques

Author: Prabhakar S. Naidu

Publisher: CRC Press

ISBN: 9780849324642

Category: Mathematics

Page: 416

View: 7908

Spectrum analysis can be considered as a topic in statistics as well as a topic in digital signal processing (DSP). This book takes a middle course by emphasizing the time series models and their impact on spectrum analysis. The text begins with elements of probability theory and goes on to introduce the theory of stationary stochastic processes. The depth of coverage is extensive. Many topics of concern to spectral characterization of Gaussian and non-Gaussian time series, scalar and vector time series are covered. A section is devoted to the emerging areas of non-stationary and cyclostationary time series. The book is organized more as a textbook than a reference book. Each chapter includes many examples to illustrate the concepts described. Several exercises are included at the end of each chapter. The level is appropriate for graduate and research students.

Analysis of Time Series Structure

SSA and Related Techniques

Author: Nina Golyandina,Vladimir Nekrutkin,Anatoly A Zhigljavsky

Publisher: CRC Press

ISBN: 9781420035841

Category: Mathematics

Page: 320

View: 4920

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.

Time Series: Theory and Methods

Author: Peter J. Brockwell,Richard A. Davis

Publisher: Springer Science & Business Media

ISBN: 1489900047

Category: Mathematics

Page: 520

View: 5990

We have attempted in this book to give a systematic account of linear time series models and their application to the modelling and prediction of data collected sequentially in time. The aim is to provide specific techniques for handling data and at the same time to provide a thorough understanding of the mathematical basis for the techniques. Both time and frequency domain methods are discussed but the book is written in such a way that either approach could be emphasized. The book is intended to be a text for graduate students in statistics, mathematics, engineering, and the natural or social sciences. It has been used both at the M. S. level, emphasizing the more practical aspects of modelling, and at the Ph. D. level, where the detailed mathematical derivations of the deeper results can be included. Distinctive features of the book are the extensive use of elementary Hilbert space methods and recursive prediction techniques based on innovations, use of the exact Gaussian likelihood and AIC for inference, a thorough treatment of the asymptotic behavior of the maximum likelihood estimators of the coefficients of univariate ARMA models, extensive illustrations of the tech niques by means of numerical examples, and a large number of problems for the reader. The companion diskette contains programs written for the IBM PC, which can be used to apply the methods described in the text.

Spectral Analysis of Signals

The Missing Data Case

Author: Yanwei Wang,Jian Li,Petre Stoica

Publisher: Morgan & Claypool Publishers

ISBN: 1598290010

Category: Technology & Engineering

Page: 102

View: 4817

Spectral estimation is important in many fields including astronomy, meteorology, seismology, communications, economics, speech analysis, medical imaging, radar, sonar, and underwater acoustics. Most existing spectral estimation algorithms are devised for uniformly sampled complete-data sequences. However, the spectral estimation for data sequences with missing samples is also important in many applications ranging from astronomical time series analysis to synthetic aperture radar imaging with angular diversity. For spectral estimation in the missing-data case, the challenge is how to extend the existing spectral estimation techniques to deal with these missing-data samples. Recently, nonparametric adaptive filtering based techniques have been developed successfully for various missing-data problems. Collectively, these algorithms provide a comprehensive toolset for the missing-data problem based exclusively on the nonparametric adaptive filter-bank approaches, which are robust and accurate, and can provide high resolution and low sidelobes. In this book, we present these algorithms for both one-dimensional and two-dimensional spectral estimation problems.

Time-Series Forecasting

Author: Chris Chatfield

Publisher: CRC Press

ISBN: 1420036203

Category: Mathematics

Page: 280

View: 2288

From the author of the bestselling "Analysis of Time Series," Time-Series Forecasting offers a comprehensive, up-to-date review of forecasting methods. It provides a summary of time-series modelling procedures, followed by a brief catalogue of many different time-series forecasting methods, ranging from ad-hoc methods through ARIMA and state-space modelling to multivariate methods and including recent arrivals, such as GARCH models, neural networks, and cointegrated models. The author compares the more important methods in terms of their theoretical inter-relationships and their practical merits. He also considers two other general forecasting topics that have been somewhat neglected in the literature: the computation of prediction intervals and the effect of model uncertainty on forecast accuracy. Although the search for a "best" method continues, it is now well established that no single method will outperform all other methods in all situations-the context is crucial. Time-Series Forecasting provides an outstanding reference source for the more generally applicable methods particularly useful to researchers and practitioners in forecasting in the areas of economics, government, industry, and commerce.

Time Series Analysis and Its Applications

With R Examples

Author: Robert H. Shumway,David S. Stoffer

Publisher: Springer

ISBN: 3319524526

Category: Mathematics

Page: 562

View: 3942

The fourth edition of this popular graduate textbook, like its predecessors, presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using nontrivial data illustrate solutions to problems such as discovering natural and anthropogenic climate change, evaluating pain perception experiments using functional magnetic resonance imaging, and monitoring a nuclear test ban treaty. The book is designed as a textbook for graduate level students in the physical, biological, and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels. In addition to coverage of classical methods of time series regression, ARIMA models, spectral analysis and state-space models, the text includes modern developments including categorical time series analysis, multivariate spectral methods, long memory series, nonlinear models, resampling techniques, GARCH models, ARMAX models, stochastic volatility, wavelets, and Markov chain Monte Carlo integration methods. This edition includes R code for each numerical example in addition to Appendix R, which provides a reference for the data sets and R scripts used in the text in addition to a tutorial on basic R commands and R time series. An additional file is available on the book’s website for download, making all the data sets and scripts easy to load into R.

Sensor Array Signal Processing, Second Edition

Author: Prabhakar S. Naidu

Publisher: CRC Press

ISBN: 1439883130

Category: Technology & Engineering

Page: 556

View: 7266

Since publication of the first edition of Sensor Array Signal Processing in 2000, the field it heralded has come of age. Sensor arrays helped usher in the age of wireless communication by meeting the increasing capacity requirements of ever growing wireless networks, but that is only one example of the number of uses served by this valuable technology across any number of fields. Extensively updated and expanded, Sensor Array Signal Processing, Second Edition covers a wide range of interrelated topics in array processing to provide an introduction to the field that one will not find in the literature. The book introduces new developments in the use of sensors in wireless networks and the use of distributed sensors for localization. It unravels layers of complexity to explore underlying basic principles of array signal processing, focusing on the common threads that exist in wavefield analysis, rather than on particular applications. Following an introduction to the basic equations governing different wavefields, the text provides updated coverage on current topics of interest. It analyzes various types of sensor configurations; focusing on those most useful for understanding array systems in practice — uniform linear and circular arrays. Fully updated with over 150 new pages, this new edition: Includes new chapters — emphasizing the use of sensor arrays in wireless communication and localization Adds new exercises and examples to the end of each chapter Provides information on emerging topics covering, distributed sensor array, multi-component sensors, space-time processing, azimuth/elevation estimation, wideband adaptive beamformation, and frequency invariant beamformation An invaluable tool for self-study, this book provides those working in or interested in medical imaging, astronomy, radar, communications, sonar, seismology or any field that studies propagating wavefields, with a highly accessible guide. It describes each concept in precise mathematical language complete with numerical examples, detailed illustrations, and practice exercises at the end of each chapter to reinforce concepts. As with the first edition, this volume also meets the needs of professors wishing to adopt the book for graduate-level courses in telecommunications and electrical engineering.

Computer Vision

Algorithms and Applications

Author: Richard Szeliski

Publisher: Springer Science & Business Media

ISBN: 9781848829350

Category: Computers

Page: 812

View: 1385

Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images. It also describes challenging real-world applications where vision is being successfully used, both for specialized applications such as medical imaging, and for fun, consumer-level tasks such as image editing and stitching, which students can apply to their own personal photos and videos. More than just a source of “recipes,” this exceptionally authoritative and comprehensive textbook/reference also takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene. These problems are also analyzed using statistical models and solved using rigorous engineering techniques. Topics and features: structured to support active curricula and project-oriented courses, with tips in the Introduction for using the book in a variety of customized courses; presents exercises at the end of each chapter with a heavy emphasis on testing algorithms and containing numerous suggestions for small mid-term projects; provides additional material and more detailed mathematical topics in the Appendices, which cover linear algebra, numerical techniques, and Bayesian estimation theory; suggests additional reading at the end of each chapter, including the latest research in each sub-field, in addition to a full Bibliography at the end of the book; supplies supplementary course material for students at the associated website, http://szeliski.org/Book/. Suitable for an upper-level undergraduate or graduate-level course in computer science or engineering, this textbook focuses on basic techniques that work under real-world conditions and encourages students to push their creative boundaries. Its design and exposition also make it eminently suitable as a unique reference to the fundamental techniques and current research literature in computer vision.

Digital Media Processing

DSP Algorithms Using C

Author: Hazarathaiah Malepati

Publisher: Newnes

ISBN: 9780080957197

Category: Computers

Page: 768

View: 6320

Multimedia processing demands efficient programming in order to optimize functionality. Data, image, audio, and video processing, some or all of which are present in all electronic devices today, are complex programming environments. Optimized algorithms (step-by-step directions) are difficult to create but can make all the difference when developing a new application. This book discusses the most current algorithms available that will maximize your programming keeping in mind the memory and real-time constraints of the architecture with which you are working. A wide range of algorithms is covered detailing basic and advanced multimedia implementations, along with, cryptography, compression, and data error correction. The general implementation concepts can be integrated into many architectures that you find yourself working with on a specific project. Analog Devices' BlackFin technology is used for examples throughout the book. Discusses how to decrease algorithm development times to streamline your programming Covers all the latest algorithms needed for contrained systems Includes case studies on WiMAX, GPS, and portable media players

Food Analysis

Author: S. Suzanne Nielsen

Publisher: Springer

ISBN: 3319457764

Category: Technology & Engineering

Page: 649

View: 7975

This fifth edition provides information on techniques needed to analyze foods for chemical and physical properties. The book is ideal for undergraduate courses in food analysis and is also an invaluable reference to professionals in the food industry. General information chapters on regulations, labeling, sampling, and data handling provide background information for chapters on specific methods to determine chemical composition and characteristics, physical properties, and objectionable matter and constituents. Methods of analysis covered include information on the basic principles, advantages, limitations, and applications. Sections on spectroscopy and chromatography along with chapters on techniques such as immunoassays, thermal analysis, and microscopy from the perspective of their use in food analysis have been expanded. Instructors who adopt the textbook can contact the editor for access to a website with related teaching materials.

Analysis of Financial Time Series

Author: Ruey S. Tsay

Publisher: John Wiley & Sons

ISBN: 0471746185

Category: Business & Economics

Page: 576

View: 6114

Provides statistical tools and techniques needed to understand today's financial markets The Second Edition of this critically acclaimed text provides a comprehensive and systematic introduction to financial econometric models and their applications in modeling and predicting financial time series data. This latest edition continues to emphasize empirical financial data and focuses on real-world examples. Following this approach, readers will master key aspects of financial time series, including volatility modeling, neural network applications, market microstructure and high-frequency financial data, continuous-time models and Ito's Lemma, Value at Risk, multiple returns analysis, financial factor models, and econometric modeling via computation-intensive methods. The author begins with the basic characteristics of financial time series data, setting the foundation for the three main topics: Analysis and application of univariate financial time series Return series of multiple assets Bayesian inference in finance methods This new edition is a thoroughly revised and updated text, including the addition of S-Plus® commands and illustrations. Exercises have been thoroughly updated and expanded and include the most current data, providing readers with more opportunities to put the models and methods into practice. Among the new material added to the text, readers will find: Consistent covariance estimation under heteroscedasticity and serial correlation Alternative approaches to volatility modeling Financial factor models State-space models Kalman filtering Estimation of stochastic diffusion models The tools provided in this text aid readers in developing a deeper understanding of financial markets through firsthand experience in working with financial data. This is an ideal textbook for MBA students as well as a reference for researchers and professionals in business and finance.

The Analysis of Time Series

An Introduction, Sixth Edition

Author: Chris Chatfield

Publisher: CRC Press

ISBN: 9780203491683

Category: Mathematics

Page: 352

View: 2722

Since 1975, The Analysis of Time Series: An Introduction has introduced legions of statistics students and researchers to the theory and practice of time series analysis. With each successive edition, bestselling author Chris Chatfield has honed and refined his presentation, updated the material to reflect advances in the field, and presented interesting new data sets. The sixth edition is no exception. It provides an accessible, comprehensive introduction to the theory and practice of time series analysis. The treatment covers a wide range of topics, including ARIMA probability models, forecasting methods, spectral analysis, linear systems, state-space models, and the Kalman filter. It also addresses nonlinear, multivariate, and long-memory models. The author has carefully updated each chapter, added new discussions, incorporated new datasets, and made those datasets available for download from www.crcpress.com. A free online appendix on time series analysis using R can be accessed at http://people.bath.ac.uk/mascc/TSA.usingR.doc. Highlights of the Sixth Edition: A new section on handling real data New discussion on prediction intervals A completely revised and restructured chapter on more advanced topics, with new material on the aggregation of time series, analyzing time series in finance, and discrete-valued time series A new chapter of examples and practical advice Thorough updates and revisions throughout the text that reflect recent developments and dramatic changes in computing practices over the last few years The analysis of time series can be a difficult topic, but as this book has demonstrated for two-and-a-half decades, it does not have to be daunting. The accessibility, polished presentation, and broad coverage of The Analysis of Time Series make it simply the best introduction to the subject available.

Numerical Methods

Design, Analysis, and Computer Implementation of Algorithms

Author: Anne Greenbaum,Timothy P. Chartier

Publisher: Princeton University Press

ISBN: 1400842670

Category: Mathematics

Page: 464

View: 2792

Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. Clear and concise exposition of standard numerical analysis topics Explores nontraditional topics, such as mathematical modeling and Monte Carlo methods Covers modern applications, including information retrieval and animation, and classical applications from physics and engineering Promotes understanding of computational results through MATLAB exercises Provides flexibility so instructors can emphasize mathematical or applied/computational aspects of numerical methods or a combination Includes recent results on polynomial interpolation at Chebyshev points and use of the MATLAB package Chebfun Short discussions of the history of numerical methods interspersed throughout Supplementary materials available online

Understanding Machine Learning

From Theory to Algorithms

Author: Shai Shalev-Shwartz,Shai Ben-David

Publisher: Cambridge University Press

ISBN: 1107057132

Category: Computers

Page: 409

View: 8228

Introduces machine learning and its algorithmic paradigms, explaining the principles behind automated learning approaches and the considerations underlying their usage.

The Elements of Statistical Learning

Data Mining, Inference, and Prediction

Author: Trevor Hastie,Robert Tibshirani,Jerome Friedman

Publisher: Springer Science & Business Media

ISBN: 0387216065

Category: Mathematics

Page: 536

View: 4196

During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry. The book’s coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book. This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for “wide” data (p bigger than n), including multiple testing and false discovery rates. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.

MATLAB for Neuroscientists

An Introduction to Scientific Computing in MATLAB

Author: Pascal Wallisch,Michael E. Lusignan,Marc D. Benayoun,Tanya I. Baker,Adam Seth Dickey,Nicholas G. Hatsopoulos

Publisher: Academic Press

ISBN: 0123838371

Category: Computers

Page: 570

View: 2088

MATLAB for Neuroscientists serves as the only complete study manual and teaching resource for MATLAB, the globally accepted standard for scientific computing, in the neurosciences and psychology. This unique introduction can be used to learn the entire empirical and experimental process (including stimulus generation, experimental control, data collection, data analysis, modeling, and more), and the 2nd Edition continues to ensure that a wide variety of computational problems can be addressed in a single programming environment. This updated edition features additional material on the creation of visual stimuli, advanced psychophysics, analysis of LFP data, choice probabilities, synchrony, and advanced spectral analysis. Users at a variety of levels—advanced undergraduates, beginning graduate students, and researchers looking to modernize their skills—will learn to design and implement their own analytical tools, and gain the fluency required to meet the computational needs of neuroscience practitioners. The first complete volume on MATLAB focusing on neuroscience and psychology applications Problem-based approach with many examples from neuroscience and cognitive psychology using real data Illustrated in full color throughout Careful tutorial approach, by authors who are award-winning educators with strong teaching experience

Singular Spectrum Analysis for Time Series

Author: Nina Golyandina,Anatoly Zhigljavsky

Publisher: Springer Science & Business Media

ISBN: 3642349137

Category: Mathematics

Page: 120

View: 3137

Singular spectrum analysis (SSA) is a technique of time series analysis and forecasting combining elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. SSA seeks to decompose the original series into a sum of a small number of interpretable components such as trend, oscillatory components and noise. It is based on the singular value decomposition of a specific matrix constructed upon the time series. Neither a parametric model nor stationarity are assumed for the time series. This makes SSA a model-free method and hence enables SSA to have a very wide range of applicability. The present book is devoted to the methodology of SSA and shows how to use SSA both safely and with maximum effect. Potential readers of the book include: professional statisticians and econometricians, specialists in any discipline in which problems of time series analysis and forecasting occur, specialists in signal processing and those needed to extract signals from noisy data, and students taking courses on applied time series analysis.

Data Mining: Concepts and Techniques

Author: Jiawei Han,Jian Pei,Micheline Kamber

Publisher: Elsevier

ISBN: 9780123814807

Category: Computers

Page: 744

View: 3304

Data Mining: Concepts and Techniques provides the concepts and techniques in processing gathered data or information, which will be used in various applications. Specifically, it explains data mining and the tools used in discovering knowledge from the collected data. This book is referred as the knowledge discovery from data (KDD). It focuses on the feasibility, usefulness, effectiveness, and scalability of techniques of large data sets. After describing data mining, this edition explains the methods of knowing, preprocessing, processing, and warehousing data. It then presents information about data warehouses, online analytical processing (OLAP), and data cube technology. Then, the methods involved in mining frequent patterns, associations, and correlations for large data sets are described. The book details the methods for data classification and introduces the concepts and methods for data clustering. The remaining chapters discuss the outlier detection and the trends, applications, and research frontiers in data mining. This book is intended for Computer Science students, application developers, business professionals, and researchers who seek information on data mining. Presents dozens of algorithms and implementation examples, all in pseudo-code and suitable for use in real-world, large-scale data mining projects Addresses advanced topics such as mining object-relational databases, spatial databases, multimedia databases, time-series databases, text databases, the World Wide Web, and applications in several fields Provides a comprehensive, practical look at the concepts and techniques you need to get the most out of your data