Model misspecification tests, model building and predictability in complex systems

Physica D: Nonlinear Phenomena

Volumn 93, Issue 1-2, 1996, Pages 78-100

  Manuca, Radu ^a   Savit, Robert ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002245104     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(95)00283-9     Document Type: Article

References (13)

1. Some previous work on using various criteria as guides to a good reconstruction space include A. Fraser and H. Swinney, Phys. Rev. A 33 (1986) 1134;
2. A. Fraser, Physica D 34 (1989) 391, who use informational criteria;
3. M. Casdagli, S. Eubank, J. Farmer and J. Gibson Physica D 51 (1991) 52 use geometrical criteria such as minimal distortion to indicate a good reconstruction. These references differ from our work, in the criteria used for optimality, and in the range of possibilities for the reconstruction directions.
4. F. Takens, in: Dynamical Systems and Turbulence, D. Rand and L. Young, eds. (Springer, Berlin, 1981) p. 366.
5. W Brock, W. Dechert and J. Scheinkman, A Test for Independence Based on the Correlation Dimension, Technical Report 8702, SSRI, University of Wisconsin (1987).
6. R. Savit and M. Green, Physica D 50 (1991) 95;
7. M. Green and R. Savit, Physica D 50 (1991) 521.
8. J. Theiler and S. Eubank, Chaos 3 (1993) 771.
9. B. Efron and R. Tibshirani, Stat. Sci. 1 (1986) 54;
10. J. Theiler, B. Galdrikian, A. Longtin, S. Eubank and J. Farmer, Using surrogate data to detect nonlinearity in time series, in: Nonlinear Modeling and Forecasting, eds. M. Casdagli and S. Eubank (Addison-Wesley, Reading, MA, 1992) p. 163;
11. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian and J. Farmer, Physica D 58 (1992) 77.
12. N. Gershenfeld and A. Weigend, The future of time series: learning and understanding, in: Time Series Prediction: Forecasting the Future and Understanding the Past, eds. A. Weigend and N. Gershenfeld, Santa Fe Institute Studies in the Sciences of Complexity (Addison-Wesley, 1993), especially p. 10.
13. K. Wu, R. Savit and W. Brock, Physica D 69 (1993) 172.