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Author: Jan Beran Publisher: Springer ISBN: 3319743805 Category : Mathematics Languages : en Pages : 307
Book Description
This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.
Author: Jan Beran Publisher: Springer ISBN: 3319743805 Category : Mathematics Languages : en Pages : 307
Book Description
This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.
Author: Mohsen Pourahmadi Publisher: John Wiley & Sons ISBN: 9780471394341 Category : Mathematics Languages : en Pages : 446
Book Description
Foundations of time series for researchers and students This volume provides a mathematical foundation for time seriesanalysis and prediction theory using the idea of regression and thegeometry of Hilbert spaces. It presents an overview of the tools oftime series data analysis, a detailed structural analysis ofstationary processes through various reparameterizations employingtechniques from prediction theory, digital signal processing, andlinear algebra. The author emphasizes the foundation and structureof time series and backs up this coverage with theory andapplication. End-of-chapter exercises provide reinforcement for self-study andappendices covering multivariate distributions and Bayesianforecasting add useful reference material. Further coveragefeatures: * Similarities between time series analysis and longitudinal dataanalysis * Parsimonious modeling of covariance matrices through ARMA-likemodels * Fundamental roles of the Wold decomposition andorthogonalization * Applications in digital signal processing and Kalmanfiltering * Review of functional and harmonic analysis and predictiontheory Foundations of Time Series Analysis and Prediction Theory guidesreaders from the very applied principles of time series analysisthrough the most theoretical underpinnings of prediction theory. Itprovides a firm foundation for a widely applicable subject forstudents, researchers, and professionals in diverse scientificfields.
Author: Richard Johnsonbaugh Publisher: Courier Corporation ISBN: 0486134776 Category : Mathematics Languages : en Pages : 450
Book Description
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
Author: L. H. Koopmans Publisher: Academic Press ISBN: 1483218546 Category : Mathematics Languages : en Pages : 382
Book Description
The Spectral Analysis of Time Series describes the techniques and theory of the frequency domain analysis of time series. The book discusses the physical processes and the basic features of models of time series. The central feature of all models is the existence of a spectrum by which the time series is decomposed into a linear combination of sines and cosines. The investigator can used Fourier decompositions or other kinds of spectrals in time series analysis. The text explains the Wiener theory of spectral analysis, the spectral representation for weakly stationary stochastic processes, and the real spectral representation. The book also discusses sampling, aliasing, discrete-time models, linear filters that have general properties with applications to continuous-time processes, and the applications of multivariate spectral models. The text describes finite parameter models, the distribution theory of spectral estimates with applications to statistical inference, as well as sampling properties of spectral estimates, experimental design, and spectral computations. The book is intended either as a textbook or for individual reading for one-semester or two-quarter course for students of time series analysis users. It is also suitable for mathematicians or professors of calculus, statistics, and advanced mathematics.
Author: Robert H. Shumway Publisher: Springer ISBN: 3319524526 Category : Mathematics Languages : en Pages : 567
Book Description
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.
Author: Robert H. Shumway Publisher: Springer Science & Business Media ISBN: 1475732619 Category : Mathematics Languages : en Pages : 560
Book Description
A balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using non-trivial data illustrate solutions to problems, such as evaluating pain perception experiments using magnetic resonance imaging or monitoring a nuclear test ban treaty. Although designed as a text for graduate level students in statistics and the physical, biological and social sciences, some parts of the book will also serve as an undergraduate introductory course. Theory and methodology are separated to allow presentations on different levels, and the material has been updated by adding modern developments involving categorical time series analysis and the spectral envelope, multivariate spectral methods, long memory series, nonlinear models, longitudinal data analysis, resampling techniques, ARCH models, stochastic volatility, wavelets and Monte Carlo Markov chain integration methods. The book is supplemented by data and an exploratory time series analysis program ASTSA for Windows that can be downloaded from the Web as freeware.
Author: Wayne A. Woodward Publisher: CRC Press ISBN: 1498734278 Category : Mathematics Languages : en Pages : 635
Book Description
Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis. Features Gives readers the ability to actually solve significant real-world problems Addresses many types of nonstationary time series and cutting-edge methodologies Promotes understanding of the data and associated models rather than viewing it as the output of a "black box" Provides the R package tswge available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website. Over 150 exercises and extensive support for instructors The second edition includes additional real-data examples, uses R-based code that helps students easily analyze data, generate realizations from models, and explore the associated characteristics. It also adds discussion of new advances in the analysis of long memory data and data with time-varying frequencies (TVF).
Author: Peter J. Brockwell Publisher: Springer Science & Business Media ISBN: 038721657X Category : Computers Languages : en Pages : 437
Book Description
This is an introduction to time series that emphasizes methods and analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills. Statisticians and students will learn the latest methods in time series and forecasting, along with modern computational models and algorithms.
Author: Peter J. Brockwell Publisher: Springer Science & Business Media ISBN: 1489900047 Category : Mathematics Languages : en Pages : 532
Book Description
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.
Author: Jan Beran
Author: Jan Beran
Author: Mohsen Pourahmadi
Author: Richard Johnsonbaugh
Author: L. H. Koopmans
Author: Peter James Lambert
Author: Robert H. Shumway
Author: Robert H. Shumway
Author: Wayne A. Woodward
Author: Peter J. Brockwell
Author: Peter J. Brockwell