Robust and Nonlinear Time Series Analysis: Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983
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| Weitere Verfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer US
1984
|
| Schriftenreihe: | Lecture Notes in Statistics
26 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide-sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view because it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specification. They have none-the-less stressed the importance of such optimality results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assumed model |
| Beschreibung: | 1 Online-Ressource (286p) |
| ISBN: | 9781461578215 9780387961026 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4615-7821-5 |
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| 500 | |a Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide-sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view because it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specification. They have none-the-less stressed the importance of such optimality results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assumed model | ||
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Datensatz im Suchindex
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| discipline | Mathematik |
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| spelling | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 edited by Jürgen Franke, Wolfgang Härdle, Douglas Martin New York, NY Springer US 1984 1 Online-Ressource (286p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 26 0930-0325 Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide-sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view because it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specification. They have none-the-less stressed the importance of such optimality results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assumed model Statistics Statistics, general Statistik Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd rswk-swf Nichtlineare Analysis (DE-588)4177490-5 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1983 Heidelberg gnd-content 2\p (DE-588)1071861417 Konferenzschrift gnd-content Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 s 3\p DE-604 Zeitreihenanalyse (DE-588)4067486-1 s 4\p DE-604 Nichtlineare Analysis (DE-588)4177490-5 s 5\p DE-604 Franke, Jürgen 1952- (DE-588)141577177 edt Härdle, Wolfgang 1953- (DE-588)110357116 edt Martin, Douglas edt Lecture Notes in Statistics 26 (DE-604)BV036592911 26 https://doi.org/10.1007/978-1-4615-7821-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 Lecture Notes in Statistics Statistics Statistics, general Statistik Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| subject_GND | (DE-588)4276267-4 (DE-588)4177490-5 (DE-588)4067486-1 (DE-588)1071861417 |
| title | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 |
| title_auth | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 |
| title_exact_search | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 |
| title_full | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 edited by Jürgen Franke, Wolfgang Härdle, Douglas Martin |
| title_fullStr | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 edited by Jürgen Franke, Wolfgang Härdle, Douglas Martin |
| title_full_unstemmed | Robust and Nonlinear Time Series Analysis Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 edited by Jürgen Franke, Wolfgang Härdle, Douglas Martin |
| title_short | Robust and Nonlinear Time Series Analysis |
| title_sort | robust and nonlinear time series analysis proceedings of a workshop organized by the sonderforschungsbereich 123 stochastische mathematische modelle heidelberg 1983 |
| title_sub | Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 |
| topic | Statistics Statistics, general Statistik Nichtlineare Zeitreihenanalyse (DE-588)4276267-4 gnd Nichtlineare Analysis (DE-588)4177490-5 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd |
| topic_facet | Statistics Statistics, general Statistik Nichtlineare Zeitreihenanalyse Nichtlineare Analysis Zeitreihenanalyse Konferenzschrift 1983 Heidelberg Konferenzschrift |
| url | https://doi.org/10.1007/978-1-4615-7821-5 |
| volume_link | (DE-604)BV036592911 |
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