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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)
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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.
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.
 Summary
 "Ninety percent of inspiration is perspiration. " [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of singlevalued 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 inputoutput connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finiteorder 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 finiteparameter 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 WienerIt(') integrals and gave a sufficient condition for the second order stationarity. An impor tant
 Language

 eng
 eng
 Edition
 1st ed. 1999.
 Extent
 1 online resource (XV, 270 p. 25 illus.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 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 WienerItô Integral
 2.1 Functions of Spaces $$ \overline {L_{\Phi }^{n}} $$ and $$ \widetilde{{L_{\Phi }^{n}}} $$
 2.2 The multiple WienerItô Integral of second order
 2.3 The multiple WienerItô 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 multiplebilinear models
 3.5 State space realization
 3.6 Some bilinear models of interest
 3.7 Identification of GARCH(1,1) Model
 4 NonGaussian Estimation
 4.1 Estimating a parameter for nonGaussian 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 NonGaussian Estimation
 E.0.1 Proof for Section 4.4
 Appendix F Proof for the Chapter Linearity Test
 References
 Isbn
 9781461215523
 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
 Language

 eng
 eng
 Summary
 "Ninety percent of inspiration is perspiration. " [31] The Wiener approach to nonlinear stochastic systems [146] permits the representation of singlevalued 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 inputoutput connections. Although, theoretically, these representations are elegant, in practice it is not feasible to estimate all the finiteorder 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 finiteparameter 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 WienerIt(') integrals and gave a sufficient condition for the second order stationarity. An impor tant
 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
 T5757.97
 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)
 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 WienerItô Integral  2.1 Functions of Spaces $$ \overline {L_{\Phi }^{n}} $$ and $$ \widetilde{{L_{\Phi }^{n}}} $$  2.2 The multiple WienerItô Integral of second order  2.3 The multiple WienerItô 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 multiplebilinear models  3.5 State space realization  3.6 Some bilinear models of interest  3.7 Identification of GARCH(1,1) Model  4 NonGaussian Estimation  4.1 Estimating a parameter for nonGaussian 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 NonGaussian 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
 10.1007/9781461215523
 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
 (DEHe213)9781461215523
 (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)
 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 WienerItô Integral  2.1 Functions of Spaces $$ \overline {L_{\Phi }^{n}} $$ and $$ \widetilde{{L_{\Phi }^{n}}} $$  2.2 The multiple WienerItô Integral of second order  2.3 The multiple WienerItô 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 multiplebilinear models  3.5 State space realization  3.6 Some bilinear models of interest  3.7 Identification of GARCH(1,1) Model  4 NonGaussian Estimation  4.1 Estimating a parameter for nonGaussian 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 NonGaussian 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
 10.1007/9781461215523
 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
 (DEHe213)9781461215523
 (MiAaPQ)EBC3076075
 (EXLCZ)993400000000089597
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