The Resource Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach, by György Terdik, (electronic resource)

Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach, by György Terdik, (electronic resource) Resource Information The item Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach, by György Terdik, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.

Label
Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach
Title
Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis
Title remainder
A Frequency Domain Approach
Statement of responsibility
by György Terdik
Creator
Author
Author
Subject
Language
• eng
• eng
Summary
"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
Member of
Terdik, György
Dewey number
519
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
qIMnIjdy55o
Image bit depth
0
Language note
English
LC call number
T57-57.97
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Lecture Notes in Statistics,
Series volume
142
• Mathematics
• Applications of Mathematics
Label
Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach, by György Terdik, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
• cr
Color
not applicable
Content category
text
Content type code
• txt
Contents
1 Foundations -- 1.1 Expectation of Nonlinear Functions of Gaussian Variables -- 1.2 Hermite Polynomials -- 1.3 Cumulants -- 1.4 Diagrams, and Moments and Cumulants for Gaussian Systems -- 1.5 Stationary processes and spectra -- 2 The Multiple Wiener-Itô Integral -- 2.1 Functions of Spaces $$\overline {L_{\Phi }^{n}}$$ and $$\widetilde{{L_{\Phi }^{n}}}$$ -- 2.2 The multiple Wiener-Itô Integral of second order -- 2.3 The multiple Wiener-Itô integral of order n -- 2.4 Chaotic representation of stationary processes -- 3 Stationary Bilinear Models -- 3.1 Definition of bilinear models -- 3.2 Identification of a bilinear model with scalar states -- 3.3 Identification of bilinear processes, general case -- 3.4 Identification of multiple-bilinear models -- 3.5 State space realization -- 3.6 Some bilinear models of interest -- 3.7 Identification of GARCH(1,1) Model -- 4 Non-Gaussian Estimation -- 4.1 Estimating a parameter for non-Gaussian data -- 4.2 Consistency and asymptotic variance of the estimate -- 4.3 Asymptotic normality of the estimate -- 4.4 Asymptotic variance in the case of linear processes -- 5 Linearity Test -- 5.1 Quadratic predictor -- 5.2 The test statistics -- 5.3 Comments on computing the test statistics -- 5.4 Simulations and real data -- 6 Some Applications -- 6.1 Testing linearity -- 6.2 Bilinear fitting -- Appendix A Moments -- Appendix B Proofs for the Chapter Stationary Bilinear Models -- Appendix C Proofs for Section 3.6.1 -- Appendix D Cumulants and Fourier Transforms for GARCH(1,1) -- Appendix E Proofs for the Chapter Non-Gaussian Estimation -- E.0.1 Proof for Section 4.4 -- Appendix F Proof for the Chapter Linearity Test -- References
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (XV, 270 p. 25 illus.)
File format
multiple file formats
Form of item
online
Isbn
9781461215523
Level of compression
uncompressed
Media category
computer
Media type code
• c
Other control number
10.1007/978-1-4612-1552-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
• (CKB)3400000000089597
• (SSID)ssj0001296003
• (PQKBManifestationID)11754016
• (PQKBTitleCode)TC0001296003
• (PQKBWorkID)11347146
• (PQKB)10181516
• (DE-He213)978-1-4612-1552-3
• (MiAaPQ)EBC3076075
• (EXLCZ)993400000000089597
Label
Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis : A Frequency Domain Approach, by György Terdik, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
• cr
Color
not applicable
Content category
text
Content type code
• txt
Contents
1 Foundations -- 1.1 Expectation of Nonlinear Functions of Gaussian Variables -- 1.2 Hermite Polynomials -- 1.3 Cumulants -- 1.4 Diagrams, and Moments and Cumulants for Gaussian Systems -- 1.5 Stationary processes and spectra -- 2 The Multiple Wiener-Itô Integral -- 2.1 Functions of Spaces $$\overline {L_{\Phi }^{n}}$$ and $$\widetilde{{L_{\Phi }^{n}}}$$ -- 2.2 The multiple Wiener-Itô Integral of second order -- 2.3 The multiple Wiener-Itô integral of order n -- 2.4 Chaotic representation of stationary processes -- 3 Stationary Bilinear Models -- 3.1 Definition of bilinear models -- 3.2 Identification of a bilinear model with scalar states -- 3.3 Identification of bilinear processes, general case -- 3.4 Identification of multiple-bilinear models -- 3.5 State space realization -- 3.6 Some bilinear models of interest -- 3.7 Identification of GARCH(1,1) Model -- 4 Non-Gaussian Estimation -- 4.1 Estimating a parameter for non-Gaussian data -- 4.2 Consistency and asymptotic variance of the estimate -- 4.3 Asymptotic normality of the estimate -- 4.4 Asymptotic variance in the case of linear processes -- 5 Linearity Test -- 5.1 Quadratic predictor -- 5.2 The test statistics -- 5.3 Comments on computing the test statistics -- 5.4 Simulations and real data -- 6 Some Applications -- 6.1 Testing linearity -- 6.2 Bilinear fitting -- Appendix A Moments -- Appendix B Proofs for the Chapter Stationary Bilinear Models -- Appendix C Proofs for Section 3.6.1 -- Appendix D Cumulants and Fourier Transforms for GARCH(1,1) -- Appendix E Proofs for the Chapter Non-Gaussian Estimation -- E.0.1 Proof for Section 4.4 -- Appendix F Proof for the Chapter Linearity Test -- References
Dimensions
unknown
Edition
1st ed. 1999.
Extent
1 online resource (XV, 270 p. 25 illus.)
File format
multiple file formats
Form of item
online
Isbn
9781461215523
Level of compression
uncompressed
Media category
computer
Media type code
• c
Other control number
10.1007/978-1-4612-1552-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
• (CKB)3400000000089597
• (SSID)ssj0001296003
• (PQKBManifestationID)11754016
• (PQKBTitleCode)TC0001296003
• (PQKBWorkID)11347146
• (PQKB)10181516
• (DE-He213)978-1-4612-1552-3
• (MiAaPQ)EBC3076075
• (EXLCZ)993400000000089597

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