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Gaussian and Non-Gaussian Linear Time Series and Random Fields

Author: Murray Rosenblatt

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 252

ISBN-13: 1461212626

The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.

Stationary Sequences and Random Fields

Author: Murray Rosenblatt

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 253

ISBN-13: 1461251567

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This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.

Non-Gaussian Autoregressive-Type Time Series

Author: N. Balakrishna

Publisher: Springer Nature

Published: 2022-01-27

Total Pages: 238

ISBN-13: 9811681627

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This book brings together a variety of non-Gaussian autoregressive-type models to analyze time-series data. This book collects and collates most of the available models in the field and provide their probabilistic and inferential properties. This book classifies the stationary time-series models into different groups such as linear stationary models with non-Gaussian innovations, linear stationary models with non-Gaussian marginal distributions, product autoregressive models and minification models. Even though several non-Gaussian time-series models are available in the literature, most of them are focusing on the model structure and the probabilistic properties.

Predictions in Time Series Using Regression Models

Author: Frantisek Stulajter

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 237

ISBN-13: 1475736290

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This book will interest and assist people who are dealing with the problems of predictions of time series in higher education and research. It will greatly assist people who apply time series theory to practical problems in their work and also serve as a textbook for postgraduate students in statistics economics and related subjects.

Gaussian Markov Random Fields

Author: Havard Rue

Publisher: CRC Press

Published: 2005-02-18

Total Pages: 280

ISBN-13: 0203492021

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Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie

Studies in Econometrics, Time Series, and Multivariate Statistics

Author: Samuel Karlin

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 591

ISBN-13: 1483268039

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Studies in Econometrics, Time Series, and Multivariate Statistics covers the theoretical and practical aspects of econometrics, social sciences, time series, and multivariate statistics. This book is organized into three parts encompassing 28 chapters. Part I contains studies on logit model, normal discriminant analysis, maximum likelihood estimation, abnormal selection bias, and regression analysis with a categorized explanatory variable. This part also deals with prediction-based tests for misspecification in nonlinear simultaneous systems and the identification in models with autoregressive errors. Part II highlights studies in time series, including time series analysis of error-correction models, time series model identification, linear random fields, segmentation of time series, and some basic asymptotic theory for linear processes in time series analysis. Part III contains papers on optimality properties in discrete multivariate analysis, Anderson’s probability inequality, and asymptotic distributions of test statistics. This part also presents the comparison of measures, multivariate majorization, and of experiments for some multivariate normal situations. Studies on Bayes procedures for combining independent F tests and the limit theorems on high dimensional spheres and Stiefel manifolds are included. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

Stable Non-Gaussian Random Processes

Author: Gennady Samoradnitsky

Publisher: Routledge

Published: 2017-11-22

Total Pages: 632

ISBN-13: 1351414801

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This book serves as a standard reference, making this area accessible not only to researchers in probability and statistics, but also to graduate students and practitioners. The book assumes only a first-year graduate course in probability. Each chapter begins with a brief overview and concludes with a wide range of exercises at varying levels of difficulty. The authors supply detailed hints for the more challenging problems, and cover many advances made in recent years.

Encyclopedia of Environmetrics

Author: Abdel H. El-Shaarawi

Publisher: John Wiley & Sons

Published: 2002

Total Pages: 660

ISBN-13: 9780471899976

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A comprehensive overview of environmetric research and its applications... Environmetrics covers the development and application of quantitative methods in the environmental sciences. It provides essential tools for understanding, predicting, and controlling the impacts of agents, both man-made and natural, which affect the environment. Basic and applied research in this area covers a broad range of topics. Primary among these are the quantitative sciences, such as statistics, probability and applied mathematics, chemometrics, and econometrics. Applications are also important, for example in, ecology and environmental biology, public health, atmospheric science, geology, engineering, risk management, and regulatory/governmental policy amongst others. * Divided into 12 sections, the Encyclopedia brings together over 600 detailed articles which have been carefully selected and reviewed through the collaborative efforts of the Editors-in-Chief and the appropriate Section Editor * Presented in alphabetical order all the articles will include an explanatory introduction, extensive cross-referencing and an up-to-date bibliography providing literature references for further reading. Presenting state of the art information in a readable, highly accessible style, the scope and coverage provided by the Encyclopedia of Environmetrics will ensure its place as the landmark reference for the many scientists, educators, and decision-makers working across this multidisciplinary field. An essential reference tool for university libraries, research laboratories, government institutions and consultancies concerned with the environmental sciences, the Encyclopedia of Environmetrics brings together for the first time, comprehensive coverage of the full range of topics, techniques and applications covered by this multidisciplinary field. There is currently no central reference source which addresses the needs of this multidisciplinary community. This new Encyclopedia will fill this gap by providing a comprehensive source of relevant fundamental concepts in environmetric research, development and applications for statisticians, mathematicians, economists, environmentalists, ecologist, government officials and policy makers.

Asymptotic Theory of Statistical Inference for Time Series

Author: Masanobu Taniguchi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 671

ISBN-13: 146121162X

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The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.

Selected Works of Murray Rosenblatt

Author: Richard A. Davis

Publisher: Springer Science & Business Media

Published: 2011-05-06

Total Pages: 489

ISBN-13: 1441983392

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During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. Among his many contributions, Rosenblatt conducted seminal work on density estimation, central limit theorems under strong mixing conditions, spectral domain methodology, long memory processes and Markov processes. He has published over 130 papers and 5 books, many as relevant today as when they first appeared decades ago. Murray Rosenblatt was one of the founding members of the Department of Mathematics at the University of California at San Diego (UCSD) and served as advisor to over twenty PhD students. He maintains a close association with UCSD in his role as Professor Emeritus. This volume is a celebration of Murray Rosenblatt's stellar research career that spans over six decades, and includes some of his most interesting and influential papers. Several leading experts provide commentary and reflections on various directions of Murray's research portfolio.