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)

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
http://library.link/vocab/creatorName
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
http://library.link/vocab/subjectName
  • 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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