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"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.
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Table of contents (6 chapters)
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Bibliographic Information
Book Title: Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
Book Subtitle: A Frequency Domain Approach
Authors: György Terdik
Series Title: Lecture Notes in Statistics
DOI: https://doi.org/10.1007/978-1-4612-1552-3
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 1999
Softcover ISBN: 978-0-387-98872-6Published: 30 July 1999
eBook ISBN: 978-1-4612-1552-3Published: 06 December 2012
Series ISSN: 0930-0325
Series E-ISSN: 2197-7186
Edition Number: 1
Number of Pages: XV, 270
Number of Illustrations: 25 b/w illustrations
Topics: Applications of Mathematics