Nonlinear System Theory: Another Look at Dependence
Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natura...
Veröffentlicht in: | Proceedings of the National Academy of Sciences of the United States of America. - National Academy of Sciences of the United States of America. - 102(2005), 40, Seite 14150-14154 |
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Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
2005
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Zugriff auf das übergeordnete Werk: | Proceedings of the National Academy of Sciences of the United States of America |
Schlagworte: | Nonlinear time series Limit theory Kernel estimation Weak convergence Mathematics Applied sciences Information science |
Zusammenfassung: | Based on the nonlinear system theory, we introduce previously undescribed dependence measures for stationary causal processes. Our physical and predictive dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The proposed dependence measures provide a natural framework for a limit theory for stationary processes. In particular, under conditions with quite simple forms, we present limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions are mild and easily verifiable because they are directly related to the data-generating mechanisms. |
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ISSN: | 10916490 |