Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

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Publisher : John Wiley & Sons
ISBN 13 : 1786305038
Total Pages : 308 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences by : Maksym Luz

Download or read book Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences written by Maksym Luz and published by John Wiley & Sons. This book was released on 2019-12-12 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Non-Stationary Stochastic Processes Estimation

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311132625X
Total Pages : 381 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Non-Stationary Stochastic Processes Estimation by : Maksym Luz

Download or read book Non-Stationary Stochastic Processes Estimation written by Maksym Luz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-05-20 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119663520
Total Pages : 314 pages
Book Rating : 4.1/5 (196 download)

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Book Synopsis Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences by : Maksym Luz

Download or read book Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences written by Maksym Luz and published by John Wiley & Sons. This book was released on 2019-09-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Journal of Statistical Planning and Inference

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Publisher :
ISBN 13 :
Total Pages : 1124 pages
Book Rating : 4.3/5 (758 download)

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Book Synopsis Journal of Statistical Planning and Inference by : North-Holland Publishing Company

Download or read book Journal of Statistical Planning and Inference written by North-Holland Publishing Company and published by . This book was released on 1999 with total page 1124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Abstracts of Papers Presented to the American Mathematical Society

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Publisher :
ISBN 13 :
Total Pages : 576 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Abstracts of Papers Presented to the American Mathematical Society by : American Mathematical Society

Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1987 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Current Index to Statistics, Applications, Methods and Theory

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Publisher :
ISBN 13 :
Total Pages : 948 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Current Index to Statistics, Applications, Methods and Theory by :

Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1999 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.

Non-Stationary Stochastic Processes Estimation

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111325628
Total Pages : 310 pages
Book Rating : 4.1/5 (113 download)

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Book Synopsis Non-Stationary Stochastic Processes Estimation by : Maksym Luz

Download or read book Non-Stationary Stochastic Processes Estimation written by Maksym Luz and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-05-20 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Unit Roots, Cointegration, and Structural Change

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521587822
Total Pages : 528 pages
Book Rating : 4.5/5 (878 download)

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Book Synopsis Unit Roots, Cointegration, and Structural Change by : G. S. Maddala

Download or read book Unit Roots, Cointegration, and Structural Change written by G. S. Maddala and published by Cambridge University Press. This book was released on 1998 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of unit roots, cointegration and structural change from a best-selling author.

Markov Chains

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Publisher : John Wiley & Sons
ISBN 13 : 1118731530
Total Pages : 306 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Markov Chains by : Bruno Sericola

Download or read book Markov Chains written by Bruno Sericola and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest. The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes – Bretagne Atlantique in France. His main research activity is in performance evaluation of computer and communication systems, dependability analysis of fault-tolerant systems and stochastic models.

Probability and Random Processes

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Publisher : John Wiley & Sons
ISBN 13 : 0471998281
Total Pages : 739 pages
Book Rating : 4.4/5 (719 download)

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Book Synopsis Probability and Random Processes by : Venkatarama Krishnan

Download or read book Probability and Random Processes written by Venkatarama Krishnan and published by John Wiley & Sons. This book was released on 2006-06-27 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students. Key topics covered include: * Random variables and most of their frequently used discrete andcontinuous probability distribution functions * Moments, transformations, and convergences of randomvariables * Characteristic, generating, and moment-generating functions * Computer generation of random variates * Estimation theory and the associated orthogonalityprinciple * Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts * Vector random variables * Random processes and stationarity concepts * Extensive classification of random processes * Random processes through linear systems and the associated Wienerand Kalman filters * Application of probability in single photon emission tomography(SPECT) More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem. Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale. This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.

Mathematical Modelling

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Publisher : John Wiley & Sons
ISBN 13 : 1119483999
Total Pages : 238 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Modelling by : Seyed M. Moghadas

Download or read book Mathematical Modelling written by Seyed M. Moghadas and published by John Wiley & Sons. This book was released on 2018-07-24 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important resource that provides an overview of mathematical modelling Mathematical Modelling offers a comprehensive guide to both analytical and computational aspects of mathematical modelling that encompasses a wide range of subjects. The authors provide an overview of the basic concepts of mathematical modelling and review the relevant topics from differential equations and linear algebra. The text explores the various types of mathematical models, and includes a range of examples that help to describe a variety of techniques from dynamical systems theory. The book’s analytical techniques examine compartmental modelling, stability, bifurcation, discretization, and fixed-point analysis. The theoretical analyses involve systems of ordinary differential equations for deterministic models. The text also contains information on concepts of probability and random variables as the requirements of stochastic processes. In addition, the authors describe algorithms for computer simulation of both deterministic and stochastic models, and review a number of well-known models that illustrate their application in different fields of study. This important resource: Includes a broad spectrum of models that fall under deterministic and stochastic classes and discusses them in both continuous and discrete forms Demonstrates the wide spectrum of problems that can be addressed through mathematical modelling based on fundamental tools and techniques in applied mathematics and statistics Contains an appendix that reveals the overall approach that can be taken to solve exercises in different chapters Offers many exercises to help better understand the modelling process Written for graduate students in applied mathematics, instructors, and professionals using mathematical modelling for research and training purposes, Mathematical Modelling: A Graduate Textbook covers a broad range of analytical and computational aspects of mathematical modelling.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 1208 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Time Series and Forecasting

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Publisher : Springer Science & Business Media
ISBN 13 : 1475725264
Total Pages : 429 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Time Series and Forecasting by : Peter J. Brockwell

Download or read book Introduction to Time Series and Forecasting written by Peter J. Brockwell and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introducitons are also given to cointegration and to non-linear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis.

The Theory of Stochastic Processes I

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Publisher : Springer
ISBN 13 : 3642619436
Total Pages : 587 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis The Theory of Stochastic Processes I by : Iosif I. Gikhman

Download or read book The Theory of Stochastic Processes I written by Iosif I. Gikhman and published by Springer. This book was released on 2015-03-30 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." --D.W. Stroock, Bulletin of the American Mathematical Society, 1980

Correlation Theory of Stationary and Related Random Functions

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Publisher : Springer Science & Business Media
ISBN 13 : 1461246288
Total Pages : 267 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Correlation Theory of Stationary and Related Random Functions by : A.M. Yaglom

Download or read book Correlation Theory of Stationary and Related Random Functions written by A.M. Yaglom and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.

Estimation of Stochastic Processes with Missing Observations

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Publisher :
ISBN 13 : 9781536158908
Total Pages : 0 pages
Book Rating : 4.1/5 (589 download)

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Book Synopsis Estimation of Stochastic Processes with Missing Observations by : Mikhail Moklyachuk

Download or read book Estimation of Stochastic Processes with Missing Observations written by Mikhail Moklyachuk and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose results of the investigation of the problem of mean square optimal estimation of linear functionals constructed from unobserved values of stationary stochastic processes. Estimates are based on observations of the processes with additive stationary noise process. The aim of the book is to develop methods for finding the optimal estimates of the functionals in the case where some observations are missing. Formulas for computing values of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the processes are exactly known. The minimax robust method of estimation is applied in the case of spectral uncertainty, where the spectral densities of the processes are not known exactly while some classes of admissible spectral densities are given. The formulas that determine the least favourable spectral densities and the minimax spectral characteristics of the optimal estimates of functionals are proposed for some special classes of admissible densities.

Recent Developments in Cointegration

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Publisher :
ISBN 13 : 9783038429562
Total Pages : pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Recent Developments in Cointegration by : Katarina Juselius

Download or read book Recent Developments in Cointegration written by Katarina Juselius and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Developments in Cointegration.