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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.
Originally published in 1988, The Statistical Theory of Linear Systems deals with identification (in the sense of obtaining a model from data) of multi-input and multi-output linear systems, in particular systems in ARMAX and state space form. The book emphasizes the underlying theory. It covers structure theory, in particular realization and parameterization of linear systems, with special emphasis on the analysis of properties of parameter spaces and parameterizations relevant for estimation and model selection; Gaussian maximum likelihood estimation of the real-valued parameters of linear systems, with an emphasis on asymptotic theory; model selection, in particular order estimation, by i...
This Festschrift is intended as a homage to our esteemed colleague, friend and maestro Giorgio Picci on the occasion of his sixty-?fth birthday. We have knownGiorgiosince our undergraduatestudies at the University of Padova, wherewe?rst experiencedhisfascinatingteachingin theclass ofSystem Identi?cation. While progressing through the PhD program, then continuing to collaborate with him and eventually becoming colleagues, we have had many opportunitiesto appreciate the value of Giorgio as a professor and a scientist, and chie?y as a person. We learned a lot from him and we feel indebted for his scienti?c guidance, his constant support, encouragement and enthusiasm. For these reasons we are pr...
This book is dedicated to Prof. Peter Young on his 70th birthday. Professor Young has been a pioneer in systems and control, and over the past 45 years he has influenced many developments in this field. This volume comprises a collection of contributions by leading experts in system identification, time-series analysis, environmetric modelling and control system design – modern research in topics that reflect important areas of interest in Professor Young’s research career. Recent theoretical developments in and relevant applications of these areas are explored treating the various subjects broadly and in depth. The authoritative and up-to-date research presented here will be of interest to academic researcher in control and disciplines related to environmental research, particularly those to with water systems. The tutorial style in which many of the contributions are composed also makes the book suitable as a source of study material for graduate students in those areas.
This book is based on a workshop entitled.: Model " Identification and Adap tive Control: From Windsurfing to Telecommunications" held in Sydney, Aus tralia, on December 16, 2000. The workshop was organized in honour of Pro fessor Brian (BDO) Anderson in recognition of his seminal contributions to systems science over the past 4 decades. . The chapters in the book have been written by colleagues, friends and stu dents of Brian Anderson. A central theme of the book is the inter relationship between identification and the use of models in real world applications. This theme has underpinned much of Brian Anderson's own contributions. The book reflects on these contributions as well as makirig important statements about possible future research directions. The subtitle of the book (From Windsurfing to Telecommunications) rec ognizes the fact that many common life experiences, such as those we en counter when learning to ride a windsurfer are models for design methods that can be used on real world advanced technological control problems. In deed, Brian Anderson extensively explored this link in his research work.
This handbook provides an up-to-date survey of current research topics and applications of time series analysis methods written by leading experts in their fields. It covers recent developments in univariate as well as bivariate and multivariate time series analysis techniques ranging from physics' to life sciences' applications. Each chapter comprises both methodological aspects and applications to real world complex systems, such as the human brain or Earth's climate. Covering an exceptionally broad spectrum of topics, beginners, experts and practitioners who seek to understand the latest developments will profit from this handbook.
This important book consists of surveys of high-frequency financial data analysis and econometric forecasting, written by pioneers in these areas including Nobel laureate Lawrence Klein. Some of the chapters were presented as tutorials to an audience in the Econometric Forecasting and High-Frequency Data Analysis Workshop at the Institute for Mathematical Science, National University of Singapore in May 2006. They will be of interest to researchers working in macroeconometrics as well as financial econometrics. Moreover, readers will find these chapters useful as a guide to the literature as well as suggestions for future research.
Originally published in 1970, Finite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving. The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all the while remaining impervious to change. Since linearity lies at the heart of much of the mathematical analysis used in applications, a firm grounding in its central ideas is essential. This book touches upon many of the standard topics in applied mathematics, develops the theory of linear systems in a systematic way, making as much use as possible of vector ideas, and contains a number of nontrivial examples and many exercises.
The first book of a three-volume set, Three-Dimensional Elasticity covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. It includes the known existence theorems, either via the implicit function theorem or via the minimization of the energy (John Ball’s theory). An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Statistical computing provides the link between statistical theory and applied statistics. The content of the book covers all aspects of this link, from the development and implementation of new statistical ideas to user experiences and software evaluation. The proceedings should appeal to anyone working in statistics and using computers, whether in universities, industrial companies, government agencies, research institutes or as software developers