Multidimensional Stationary Time Series

Multidimensional Stationary Time Series
Author: Marianna Bolla
Publisher: CRC Press
Total Pages: 318
Release: 2021-04-29
Genre: Mathematics
ISBN: 1000392392

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This book gives a brief survey of the theory of multidimensional (multivariate), weakly stationary time series, with emphasis on dimension reduction and prediction. Understanding the covered material requires a certain mathematical maturity, a degree of knowledge in probability theory, linear algebra, and also in real, complex and functional analysis. For this, the cited literature and the Appendix contain all necessary material. The main tools of the book include harmonic analysis, some abstract algebra, and state space methods: linear time-invariant filters, factorization of rational spectral densities, and methods that reduce the rank of the spectral density matrix. Serves to find analogies between classical results (Cramer, Wold, Kolmogorov, Wiener, Kálmán, Rozanov) and up-to-date methods for dimension reduction in multidimensional time series Provides a unified treatment for time and frequency domain inferences by using machinery of complex and harmonic analysis, spectral and Smith--McMillan decompositions. Establishes analogies between the time and frequency domain notions and calculations Discusses the Wold's decomposition and the Kolmogorov's classification together, by distinguishing between different types of singularities. Understanding the remote past helps us to characterize the ideal situation where there is a regular part at present. Examples and constructions are also given Establishes a common outline structure for the state space models, prediction, and innovation algorithms with unified notions and principles, which is applicable to real-life high frequency time series It is an ideal companion for graduate students studying the theory of multivariate time series and researchers working in this field.

Time Series Analysis

Time Series Analysis
Author: William W. S. Wei
Publisher: Addison-Wesley Longman
Total Pages: 648
Release: 2006
Genre: Mathematics
ISBN:

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With its broad coverage of methodology, this comprehensive book is a useful learning and reference tool for those in applied sciences where analysis and research of time series is useful. Its plentiful examples show the operational details and purpose of a variety of univariate and multivariate time series methods. Numerous figures, tables and real-life time series data sets illustrate the models and methods useful for analyzing, modeling, and forecasting data collected sequentially in time. The text also offers a balanced treatment between theory and applications. Overview. Fundamental Concepts. Stationary Time Series Models. Nonstationary Time Series Models. Forecasting. Model Identification. Parameter Estimation, Diagnostic Checking, and Model Selection. Seasonal Time Series Models. Testing for a Unit Root. Intervention Analysis and Outlier Detection. Fourier Analysis. Spectral Theory of Stationary Processes. Estimation of the Spectrum. Transfer Function Models. Time Series Regression and GARCH Models. Vector Time Series Models. More on Vector Time Series. State Space Models and the Kalman Filter. Long Memory and Nonlinear Processes. Aggregation and Systematic Sampling in Time Series. For all readers interested in time series analysis.

Time Series: Theory and Methods

Time Series: Theory and Methods
Author: Peter J. Brockwell
Publisher: Springer Science & Business Media
Total Pages: 532
Release: 2013-11-11
Genre: Mathematics
ISBN: 1489900047

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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.

Statistical Analysis of Stationary Time Series

Statistical Analysis of Stationary Time Series
Author: Ulf Grenander
Publisher: American Mathematical Soc.
Total Pages: 312
Release: 2008-05
Genre: Mathematics
ISBN: 0821844377

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Written in the terminology of the theoretical statistician, this book presents an approach to time series analysis. It presents a unified treatment of methods that are being used in the physical sciences and technology.

Advance Trends in Soft Computing

Advance Trends in Soft Computing
Author: Mo Jamshidi
Publisher: Springer
Total Pages: 464
Release: 2013-11-18
Genre: Technology & Engineering
ISBN: 3319036742

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This book is the proceedings of the 3rd World Conference on Soft Computing (WCSC), which was held in San Antonio, TX, USA, on December 16-18, 2013. It presents start-of-the-art theory and applications of soft computing together with an in-depth discussion of current and future challenges in the field, providing readers with a 360 degree view on soft computing. Topics range from fuzzy sets, to fuzzy logic, fuzzy mathematics, neuro-fuzzy systems, fuzzy control, decision making in fuzzy environments, image processing and many more. The book is dedicated to Lotfi A. Zadeh, a renowned specialist in signal analysis and control systems research who proposed the idea of fuzzy sets, in which an element may have a partial membership, in the early 1960s, followed by the idea of fuzzy logic, in which a statement can be true only to a certain degree, with degrees described by numbers in the interval [0,1]. The performance of fuzzy systems can often be improved with the help of optimization techniques, e.g. evolutionary computation, and by endowing the corresponding system with the ability to learn, e.g. by combining fuzzy systems with neural networks. The resulting “consortium” of fuzzy, evolutionary, and neural techniques is known as soft computing and is the main focus of this book.

Multivariate Time Series Analysis and Applications

Multivariate Time Series Analysis and Applications
Author: William W. S. Wei
Publisher: John Wiley & Sons
Total Pages: 536
Release: 2019-03-18
Genre: Mathematics
ISBN: 1119502853

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An essential guide on high dimensional multivariate time series including all the latest topics from one of the leading experts in the field Following the highly successful and much lauded book, Time Series Analysis—Univariate and Multivariate Methods, this new work by William W.S. Wei focuses on high dimensional multivariate time series, and is illustrated with numerous high dimensional empirical time series. Beginning with the fundamentalconcepts and issues of multivariate time series analysis,this book covers many topics that are not found in general multivariate time series books. Some of these are repeated measurements, space-time series modelling, and dimension reduction. The book also looks at vector time series models, multivariate time series regression models, and principle component analysis of multivariate time series. Additionally, it provides readers with information on factor analysis of multivariate time series, multivariate GARCH models, and multivariate spectral analysis of time series. With the development of computers and the internet, we have increased potential for data exploration. In the next few years, dimension will become a more serious problem. Multivariate Time Series Analysis and its Applications provides some initial solutions, which may encourage the development of related software needed for the high dimensional multivariate time series analysis. Written by bestselling author and leading expert in the field Covers topics not yet explored in current multivariate books Features classroom tested material Written specifically for time series courses Multivariate Time Series Analysis and its Applications is designed for an advanced time series analysis course. It is a must-have for anyone studying time series analysis and is also relevant for students in economics, biostatistics, and engineering.

Time Series Models

Time Series Models
Author: Manfred Deistler
Publisher: Springer Nature
Total Pages: 213
Release: 2022-10-21
Genre: Mathematics
ISBN: 3031132130

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This textbook provides a self-contained presentation of the theory and models of time series analysis. Putting an emphasis on weakly stationary processes and linear dynamic models, it describes the basic concepts, ideas, methods and results in a mathematically well-founded form and includes numerous examples and exercises. The first part presents the theory of weakly stationary processes in time and frequency domain, including prediction and filtering. The second part deals with multivariate AR, ARMA and state space models, which are the most important model classes for stationary processes, and addresses the structure of AR, ARMA and state space systems, Yule-Walker equations, factorization of rational spectral densities and Kalman filtering. Finally, there is a discussion of Granger causality, linear dynamic factor models and (G)ARCH models. The book provides a solid basis for advanced mathematics students and researchers in fields such as data-driven modeling, forecasting and filtering, which are important in statistics, control engineering, financial mathematics, econometrics and signal processing, among other subjects.

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences
Author: Maksym Luz
Publisher: John Wiley & Sons
Total Pages: 308
Release: 2019-12-12
Genre: Mathematics
ISBN: 1786305038

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Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.

Statistical Analysis of Stationary Time Series (Classic Reprint)

Statistical Analysis of Stationary Time Series (Classic Reprint)
Author: Emeritus Professor Division of Applied Mathematics Ulf Grenander
Publisher: Forgotten Books
Total Pages: 308
Release: 2017-10-28
Genre: Mathematics
ISBN: 9781527797307

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Excerpt from Statistical Analysis of Stationary Time Series These schemes have been important in the development of methods for the statistical analysis of time series. They have been used with a varying degree of success to describe many types of phenomena encountered in applications. From the discussion in Chapter 1 it Will be apparent that by using these schemes, it is possible to approximate a large and important class of stationary processes, Viz. The so-called linear processes (see For this to be possible p must take large rather than small values and para meters involved in the scheme must be adjusted adequately. During the last ten years a good deal of work has been devoted to the construction of tests, estimates and confidence intervals appropriate for these schemes. We have described a few of the more important of these results in Chapter 3. In spite of the ingenuity and great theoretical interest of some of these methods, their practical applicability seems to be limited severely by the assumption that the process is a low (usually zero, first or second) order finite parameter scheme. After surveying a good deal of the applied literature devoted to statistical analysis of time series met with in practice, we have come to the following conclusion. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Non-Stationary Stochastic Processes Estimation

Non-Stationary Stochastic Processes Estimation
Author: Maksym Luz
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 310
Release: 2024-05-20
Genre: Business & Economics
ISBN: 3111325628

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The problem of forecasting future values of economic and physical processes, the problem of restoring lost information, cleaning signals or other data observations from noise, is magnified in an information-laden word. Methods of stochastic processes estimation depend on two main factors. The first factor is construction of a model of the process being investigated. The second factor is the available information about the structure of the process under consideration. In this book, we propose results of the investigation of the problem of mean square optimal estimation (extrapolation, interpolation, and filtering) of linear functionals depending on unobserved values of stochastic sequences and processes with periodically stationary and long memory multiplicative seasonal increments. Formulas for calculating the mean square errors and the spectral characteristics of the optimal estimates of the functionals are derived in the case of spectral certainty, where spectral structure of the considered sequences and processes are exactly known. In the case where spectral densities of the sequences and processes are not known exactly while some sets of admissible spectral densities are given, we apply the minimax-robust method of estimation.