Bilinear stochastic models and related problems of nonlinear time series analysis: a frequency domain approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
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| Series: | Lecture notes in statistics
142 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 260 S. |
| ISBN: | 0387988726 |
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| 100 | 1 | |a Terdik, György |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bilinear stochastic models and related problems of nonlinear time series analysis |b a frequency domain approach |c György Terdik |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1999 | |
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Record in the Search Index
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GYOERGY TERDIK BILINEAR STOCHASTIC MODELS AND RELATED PROBLEMS OF
NONLINEAR TIME SERIES ANALYSIS A FREQUENCY DOMAIN APPROACH SPRINGER
CONTENTS LIST OF FIGURES IX INTRODUCTION XI DATA UNDER CONSIDERATION
XIII NOTATION XVII 1 FOUNDATIONS 1 1.1 EXPECTATION OF NONLINEAR
FUNCTIONS OF GAUSSIAN VARIABLES . . 1 1.2 HERMITE POLYNOMIALS 5 1.2.1
HERMITE POLYNOMIALS OF ONE VARIABLE 5 1.2.2 HERMITE POLYNOMIALS OF
SEVERAL VARIABLES 7 1.3 CUMULANTS 10 1.3.1 DEFINITION OF CUMULANTS 10
1.3.2 BASIC PROPERTIES 11 1.4 DIAGRAMS, AND MOMENTS AND CUMULANTS FOR
GAUSSIAN SYSTEMS 15 1.4.1 DIAGRAMS 15 1.4.2 MOMENTS OF GAUSSIAN SYSTEMS
16 1.4.3 CUMULANTS FOR HERMITE POLYNOMIALS 17 1.4.4 PRODUCTS FOR HERMITE
POLYNOMIALS 19 1.5 STATIONARY PROCESSES AND SPECTRA 23 1.5.1 STOCHASTIC
SPECTRAL REPRESENTATION 23 1.5.2 COMPLEX GAUSSIAN SYSTEM 25 1.5.3
SPECTRA 26 THE MULTIPLE WIENER-ITOE INTEGRAL 33 2.1 FUNCTIONS OF SPACES
L\ AND LJ 33 2.2 THE MULTIPLE WIENER-ITOE INTEGRAL OF SECOND ORDER 35
2.2.1 DEFINITION I 35 2.2.2 DEFINITION II 38 2.2.3 DEFINITION III 38 2.3
THE MULTIPLE WIENER-ITOE INTEGRAL OF ORDER N 40 2.3.1 PROPERTIES 41 2.3.2
DIAGRAM FORMULA 41 2.3.3 FOCK SPACE 44 2.3.4 STRATONOVICH INTEGRAL IN
FREQUENCY DOMAIN AND THE HU-MEYER FORMULA 45 2.4 CHAOTIC REPRESENTATION
OF STATIONARY PROCESSES 46 2.4.1 SUBORDINATED FUNCTIONALS OF GAUSSIAN
PROCESSES . 46 2.4.2 SPECTRA FOR PROCESSES WITH HERMITE DEGREE-2 49
2.4.3 THE PROCESS F (X T ) 52 STATIONARY BILINEAR MODELS 63 3.1
DEFINITION OF BILINEAR MODEIS 64 3.2 IDENTIFICATION OF A BILINEAR MODEL
WITH SCALAR STATES 66 3.2.1 MULTIPLE SPECTRAL REPRESENTATION AND
STATIONARITY . . 66 3.2.2 SPECTRA 73 3.2.3 THE NECESSARY AND SUFFICIENT
CONDITION FOR THE EXISTENCE OF THE 2NTH MOMENT, SCALAR CASE . 84 3.3
IDENTIFICATION OF BILINEAR PROCESSES, GENERAL CASE 91 3.3.1 STATE SPACE
FORM OF LOWER TRIANGULAER BILINEAR MODEIS 91 3.3.2 VECTOR VALUED BILINEAR
MODEL WITH SCALAR INPUT . 93 3.3.3 SPECTRA 96 3.3.4 NECESSARY AND
SUFFICIENT CONDITION FOR THE EXIS- TENCE OF 2N TH ORDER MOMENTS OF THE
STATE PROCESS 102 3.4 IDENTIFICATION OF MULTIPLE-BILINEAR MODEIS 107
3.4.1 CHAOTIC REPRESENTATION AND STATIONARITY 107 3.4.2 SPECTRA 119 3.5
STATE SPACE REALIZATION 124 3.5.1 THE BILINEAR REALIZATION PROBLEM 124
3.5.2 REALIZATION OF THE HERMITE DEGREE-A* HOMOGENEOUS POLYNOMIAL MODEL
127 3.5.3 MINIMAL REALIZATIONS 129 3.6 SOME BILINEAR MODEIS OF INTEREST
137 3.6.1 SIMPLE BILINEAR MODEL 137 3.6.2 HERMITE DEGREE-2 BILINEAR
MODEL 140 3.7 IDENTIFICATION OF GARCH(1,1) MODEL 145 3.7.1 SPECTRUM OF
THE STATE PROCESS 148 VII 3.7.2 SPECTRUM OF THE SQUARE OF THE
OBSERVATIONS 148 3.7.3 BISPECTRUM OF THE STATE PROCESS 149 3.7.4
BISPECTRUM OF THE PROCESS 1^ 150 3.7.5 SIMULATION 151 4 NON-GAUSSIAN
ESTIMATION 155 4.1 ESTIMATING A PARAMETER FOR NON-GAUSSIAN DATA 156 4.2
CONSISTENCY AND ASYMPTOTIC VARIANCE OF THE ESTIMATE . 162 4.3
ASYMPTOTIC NORMALITY OF THE ESTIMATE 168 4.4 ASYMPTOTIC VARIANCE IN THE
CASE OF LINEAR PROCESSES 168 4.4.1 A WORKED EXAMPLE AND SIMULATIONS 170
5 LINEARITY TEST 177 5.1 QUADRATIC PREDICTOR 178 5.1.1 QUADRATIC
PREDICTOR FOR A SIMPLE BILINEAR MODEL . . . 182 5.2 THE TEST STATISTICS
, 184 5.3 COMMENTS ON COMPUTING THE TEST STATISTICS 188 5.4 SIMULATIONS
AND REAL DATA 189 5.4.1 HOMOGENEOUS BILINEAR REALIZABLE TIME SERIES WITH
HERMITE DEGREE-2 189 5.4.2 RESULTS OF SIMULATIONS 192 6 SOME
APPLICATIONS 197 6.1 TESTING LINEARITY 197 6.1.1 GEOMAGNETIC INDICES 197
6.1.2 RESULTS OF TESTING WEAK LINEARITY FOR SIMULATED DATA ATWUECON 200
6.1.3 GARCH MODEL FITTING 201 6.2 BILINEAR FITTING 203 6.2.1 PARAMETER
ESTIMATION FOR BILINEAR PROCESSES 203 6.2.2 BILINEAR FITTING FOR REAL
DATA 206 APPENDIX A MOMENTS 211 APPENDIX B PROOFS FOR THE CHAPTER
STATIONARY BILINEAR MODELS 213 APPENDIX C PROOFS FOR SECTION 3.6.1 223
APPENDIX D CUMULANTS AND FOURIER TRANSFORMS FOR GARCH(1,1) 227 APPENDIX
E PROOFS FOR THE CHAPTER NON-GAUSSIAN ESTIMATION 231 E.0.1 PROOF FOR
SECTION 4.4 241 L9Z XAPUJ IFZ SAOUAJAJA^ QFZ ^ SA X ^I-REAUI'J JA^DET^
A\\% JOJ JOOJ J XIPUADDY I NIA |
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| isbn | 0387988726 |
| language | English |
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| physical | XX, 260 S. |
| publishDate | 1999 |
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| publisher | Springer |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Terdik, György Verfasser aut Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach György Terdik New York [u.a.] Springer 1999 XX, 260 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 142 Niet-lineaire theorieën gtt Spectrumanalyse gtt Série chronologique Séries chronologiques ram Théories non linéaires Théories non linéaires ram Tijdreeksen gtt Nonlinear theories Time-series analysis Bilineares Zeitreihenmodell (DE-588)4145512-5 gnd rswk-swf Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd rswk-swf Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 s Bilineares Zeitreihenmodell (DE-588)4145512-5 s DE-604 Lecture notes in statistics 142 (DE-604)BV002447846 142 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008679925&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Terdik, György Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach Lecture notes in statistics Niet-lineaire theorieën gtt Spectrumanalyse gtt Série chronologique Séries chronologiques ram Théories non linéaires Théories non linéaires ram Tijdreeksen gtt Nonlinear theories Time-series analysis Bilineares Zeitreihenmodell (DE-588)4145512-5 gnd Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd |
| subject_GND | (DE-588)4145512-5 (DE-588)4276267-4 |
| title | Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach |
| title_auth | Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach |
| title_exact_search | Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach |
| title_full | Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach György Terdik |
| title_fullStr | Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach György Terdik |
| title_full_unstemmed | Bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach György Terdik |
| title_short | Bilinear stochastic models and related problems of nonlinear time series analysis |
| title_sort | bilinear stochastic models and related problems of nonlinear time series analysis a frequency domain approach |
| title_sub | a frequency domain approach |
| topic | Niet-lineaire theorieën gtt Spectrumanalyse gtt Série chronologique Séries chronologiques ram Théories non linéaires Théories non linéaires ram Tijdreeksen gtt Nonlinear theories Time-series analysis Bilineares Zeitreihenmodell (DE-588)4145512-5 gnd Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd |
| topic_facet | Niet-lineaire theorieën Spectrumanalyse Série chronologique Séries chronologiques Théories non linéaires Tijdreeksen Nonlinear theories Time-series analysis Bilineares Zeitreihenmodell Nichtlineare Zeitreihenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008679925&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002447846 |
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