Local explosion modelling by non-causal process
The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework...
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| Published in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 79; no. 3; pp. 737 - 756 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Oxford
John Wiley & Sons Ltd
01.06.2017
Oxford University Press |
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| ISSN: | 1369-7412, 1467-9868 |
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| Abstract | The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behaviour of a vector of sample auto-correlations is studied in a semiparametric non-causal AR(1) framework with Pareto-like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided. |
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| AbstractList | The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behaviour of a vector of sample auto-correlations is studied in a semiparametric non-causal AR(1) framework with Pareto-like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided. Summary The non‐causal auto‐regressive process with heavy‐tailed errors has non‐linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behaviour of a vector of sample auto‐correlations is studied in a semiparametric non‐causal AR(1) framework with Pareto‐like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided. Summary The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are often observed in economic and financial time series. It provides a new model for multiple local explosions in a strictly stationary framework. The causal predictive distribution displays surprising features, such as higher moments than for the marginal distribution, or the presence of a unit root in the Cauchy case. Aggregating such models can yield complex dynamics with local and global explosion as well as variation in the rate of explosion. The asymptotic behaviour of a vector of sample auto-correlations is studied in a semiparametric non-causal AR(1) framework with Pareto-like tails, and diagnostic tests are proposed. Empirical results based on the Nasdaq composite price index are provided. |
| Author | Gouriéroux, Christian Zakoïan, Jean-Michel |
| Author_xml | – sequence: 1 givenname: Christian surname: Gourieroux fullname: Gourieroux, Christian – sequence: 2 givenname: Jean-Michel surname: Zakoian fullname: Zakoian, Jean-Michel |
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| Cites_doi | 10.1007/978-3-642-33483-2 10.1016/0927-5398(94)00015-9 10.1016/j.jspi.2009.02.007 10.1093/biomet/64.2.255 10.1214/aop/1176993074 10.1081/ETC-120039605 10.1137/1139013 10.1111/jtsa.12165 10.1214/aos/1176348677 10.1214/aos/1176349937 10.1093/biomet/74.3.535 10.1093/biomet/asm084 10.2307/2077963 10.1007/978-1-4419-0320-4 10.1086/260900 10.1111/jtsa.12139 10.1016/0304-4149(85)90216-9 10.1111/j.1468-2354.2010.00625.x 10.1111/j.1467-9892.2007.00572.x 10.1111/j.1467-9892.1992.tb00114.x 10.1214/08-AOS632 10.1093/biomet/62.1.163 10.1016/j.jeconom.2003.10.028 10.1002/9780470670057 10.1111/iere.12132 |
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| Snippet | The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles that are... Summary The non‐causal auto‐regressive process with heavy‐tailed errors has non‐linear causal dynamics, which allow for local explosion or asymmetric cycles... Summary The non-causal auto-regressive process with heavy-tailed errors has non-linear causal dynamics, which allow for local explosion or asymmetric cycles... The non‐causal auto‐regressive process with heavy‐tailed errors has non‐linear causal dynamics, which allow for local explosion or asymmetric cycles that are... |
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| SubjectTerms | Asymmetry Asymptotic properties Autocorrelation Autoregressive processes Behavior Cauchy problems Causal innovation Causality Correlation analysis Diagnostic systems diagnostic techniques Diagnostic tests Economic models Economics equations Errors Explosions Explosive bubble Global local relationship Heavy‐tailed errors Mathematical models NASDAQ trading Nonlinear dynamics Non‐causal process Price indexes prices Regression analysis Samples Stable process Statistical methods Statistics Stock market indexes Studies Time series time series analysis |
| Title | Local explosion modelling by non-causal process |
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