Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis: A Frequency Domain Approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1999
|
| Schriftenreihe: | Lecture Notes in Statistics
142 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | "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 perturbation 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 sample. 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 nonlinearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applications both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are defined 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 important |
| Beschreibung: | 1 Online-Ressource (XV, 270p) |
| ISBN: | 9781461215523 9780387988726 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-1552-3 |
Internformat
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| 245 | 1 | 0 | |a Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis |b A Frequency Domain Approach |c by György Terdik |
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| 490 | 1 | |a Lecture Notes in Statistics |v 142 |x 0930-0325 | |
| 500 | |a "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 perturbation 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 sample. 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 nonlinearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applications both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are defined 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 important | ||
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Datensatz im Suchindex
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| author | Terdik, György |
| author_facet | Terdik, György |
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| author_sort | Terdik, György |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1552-3 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461215523 9780387988726 |
| issn | 0930-0325 |
| language | English |
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| spelling | Terdik, György Verfasser aut Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis A Frequency Domain Approach by György Terdik New York, NY Springer New York 1999 1 Online-Ressource (XV, 270p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 142 0930-0325 "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 perturbation 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 sample. 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 nonlinearity in a series. Among the special classes of nonlinear models that have been studied are the bilinear processes, which have found applications both in econometrics and control theory; see, for example, Granger and Andersen [43] and Ruberti, et al. [4]. These bilinear processes are defined 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 important Statistics Statistics, general Statistik 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 1\p DE-604 Lecture Notes in Statistics 142 (DE-604)BV036592911 142 https://doi.org/10.1007/978-1-4612-1552-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Terdik, György Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis A Frequency Domain Approach Lecture Notes in Statistics Statistics Statistics, general Statistik 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 by György Terdik |
| title_fullStr | Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis A Frequency Domain Approach by György Terdik |
| title_full_unstemmed | Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis A Frequency Domain Approach by 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 | Statistics Statistics, general Statistik Bilineares Zeitreihenmodell (DE-588)4145512-5 gnd Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd |
| topic_facet | Statistics Statistics, general Statistik Bilineares Zeitreihenmodell Nichtlineare Zeitreihenanalyse |
| url | https://doi.org/10.1007/978-1-4612-1552-3 |
| volume_link | (DE-604)BV036592911 |
| work_keys_str_mv | AT terdikgyorgy bilinearstochasticmodelsandrelatedproblemsofnonlineartimeseriesanalysisafrequencydomainapproach |