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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach: 142 (Lecture Notes in Statistics, 142) - Softcover
Book 13 of 72: Lecture Notes in Statistics
Synopsis
The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Itô integrals and finally chaotic Wiener-Itô spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.
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About the Author
György Terdik received his PhD in 1982 at the Department of Probability Theory, State University of Leningrad, USSR. He has been a full-time professor at the Faculty of Informatics, University of Debrecen, Hungary since 2008. He has spent 10 semesters visiting different universities in the US including UC Berkeley and UC Santa Barbara, and the Case Western Reserve University, among others. His research interests include multivariate nonlinear statistics, time series analysis, modelling high speed communication networks, bilinear and multi-fractal models, directional statistics, and spherical processes, spatial dependence and interaction between space and time.
From the Back Cover
This book will be of interest to statistical researchers working in the area of time series.
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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach
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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -'Ninety percent of inspiration is perspiration. ' [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of single-valued systems with memory for which a small per turbation of the input produces a small perturbation of the output. The Wiener functional series representation contains many transfer functions to describe entirely the input-output connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finite-order transfer functions (or the kernels) from a finite sam ple. One of the most important classes of stochastic systems, especially from a statistical point of view, is the case when all the transfer functions are determined by finitely many parameters. Therefore, one has to seek a finite-parameter nonlinear model which can adequately represent non linearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applica tions both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are de fined to be linear in both input and output only, when either the input or output are fixed. The bilinear model was introduced by Granger and Andersen [43] and Subba Rao [118], [119]. Terdik [126] gave the solution of xii a lower triangular bilinear model in terms of multiple Wiener-It(') integrals and gave a sufficient condition for the second order stationarity. An impor tant. 288 pp. Englisch. Seller Inventory # 9780387988726
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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
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Kartoniert / Broschiert. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumula. Seller Inventory # 5913544
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 'Ninety percent of inspiration is perspiration. ' [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of single-valued systems with memory for which a small per turbation of the input produces a small perturbation of the output. The Wiener functional series representation contains many transfer functions to describe entirely the input-output connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finite-order transfer functions (or the kernels) from a finite sam ple. One of the most important classes of stochastic systems, especially from a statistical point of view, is the case when all the transfer functions are determined by finitely many parameters. Therefore, one has to seek a finite-parameter nonlinear model which can adequately represent non linearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applica tions both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are de fined to be linear in both input and output only, when either the input or output are fixed. The bilinear model was introduced by Granger and Andersen [43] and Subba Rao [118], [119]. Terdik [126] gave the solution of xii a lower triangular bilinear model in terms of multiple Wiener-It(') integrals and gave a sufficient condition for the second order stationarity. An impor tant. Seller Inventory # 9780387988726
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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach (Lecture Notes in Statistics)
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