Lecture Notes in Statistics

Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis

A Frequency Domain Approach

Authors: Terdik, György

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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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $99.00
price for USA in USD (gross)
  • ISBN 978-1-4612-1552-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA in USD
  • ISBN 978-0-387-98872-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
Book Subtitle
A Frequency Domain Approach
Authors
Series Title
Lecture Notes in Statistics
Series Volume
142
Copyright
1999
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-1552-3
DOI
10.1007/978-1-4612-1552-3
Softcover ISBN
978-0-387-98872-6
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XV, 270
Number of Illustrations
25 b/w illustrations
Topics