Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach: 142 (Lecture Notes in Statistics, 142) - Softcover

Terdik, Gy�rgy

9780387988726: Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach: 142 (Lecture Notes in Statistics, 142)

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ISBN 10: 0387988726 ISBN 13: 9780387988726

Verlag: Springer, 1999

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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-It� integrals and finally chaotic Wiener-It� spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.

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Verlag: Springer
Erscheinungsdatum: 1999
Sprache: Englisch
ISBN 10: 0387988726
ISBN 13: 9780387988726
Einband: Tapa blanda
Anzahl der Seiten: 288
Kontakt zum Hersteller: Nicht verf�gbar
Verantwortliche Person: CMN Printpool Inh. Mathis Neumann
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Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach

Gy�rgy Terdik

Verlag: Springer, Springer, 1999

ISBN 10: 0387988726 ISBN 13: 9780387988726

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Taschenbuch. Zustand: Neu. Druck auf Anfrage 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. Artikel-Nr. 9780387988726

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