# Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis

## A Frequency Domain Approach

Book

Part of the Lecture Notes in Statistics book series (LNS, volume 142)

1. Front Matter
Pages i-xx
2. György Terdik
Pages 1-31
3. György Terdik
Pages 33-62
4. György Terdik
Pages 63-153
5. György Terdik
Pages 155-176
6. György Terdik
Pages 177-195
7. György Terdik
Pages 197-209
8. Back Matter
Pages 211-260

### Introduction

"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.

### Keywords

Fitting Variance calculus statistics time series

#### Authors and affiliations

1. 1.Center for Informatics and ComputingKossuth University of DebrecenDebrecen 4010Hungary

### 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
• Copyright Information Springer-Verlag New York, Inc. 1999
• Publisher Name Springer, New York, NY
• eBook Packages
• Softcover ISBN 978-0-387-98872-6
• eBook ISBN 978-1-4612-1552-3
• Series ISSN 0930-0325
• Edition Number 1
• Number of Pages XV, 270
• Number of Illustrations 25 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site