| Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach Softcover Repri Edition Contributor(s): Terdik, György (Author) |
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ISBN: 0387988726 ISBN-13: 9780387988726 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback Published: July 1999 |
| Additional Information |
| BISAC Categories: - Mathematics | Probability & Statistics - General - Medical - Mathematics | Applied |
| Dewey: 519.55 |
| LCCN: 99023873 |
| Series: Lecture Notes in Statistics |
| Physical Information: 0.6" H x 6.14" W x 9.21" (0.90 lbs) 270 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: "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. |