Local averaging optimization for chaotic time series prediction

Neurocomputing

Volumn 48, Issue 1-4, 2002, Pages 279-297

  McNames, James ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

Chaos; Embedding dimension; Local models; Metric optimization; Time series prediction

Indexed keywords

ERROR ANALYSIS; FORECASTING; OPTIMIZATION; SIGNAL FILTERING AND PREDICTION; TIME SERIES ANALYSIS;

CROSS-VALIDATION ERRORS;

NEURAL NETWORKS;

ANALYTIC METHOD; ANALYTICAL PARAMETERS; CHAOTIC DYNAMICS; CONTROLLED STUDY; EMPIRICISM; ERROR; INTERMETHOD COMPARISON; MATHEMATICAL MODEL; PERFORMANCE; PREDICTION; PRIORITY JOURNAL; PROCESS OPTIMIZATION; REVIEW; TIME SERIES ANALYSIS; VALIDATION PROCESS;

EID: 0036825832     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(01)00647-6     Document Type: Review

References (35)

1. C.G. Atkeson, A.W. Moore, S. Schaal, Locally weighted learning, Artif. Intell. Rev. 11 (1-5) (1997) 11-73.
2. M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming: Theory and Algorithms, 2nd Edition, Wiley, New York, 1993.
3. M. Birattari, G. Bontempi, H. Bersini, Lazy learning meets the recursive least squares, in: M.S. Kearns, S.A. Solla, D.A. Cohn (Eds.), Advances in Neural Information Processing Systems, MIT Press, Cambridge, 1999, pp. 375-381.
4. G. Bontempi, M. Birattari, H. Bersini, Lazy learning for iterated time-series prediction, in: Proceedings of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling, Katholieke Universiteit Leuven, Belgium, July 1998, pp. 62-68.
5. G. Bontempi, M. Birattari, H. Bersini, Local learning for iterated time-series prediction, in: Machine Learning: Proceedings of the 16th International Conference, San Francisco, CA, 1999, pp. 32-38.
6. L. Breiman, Heuristics of instability and stabilization in model selection, The Ann. Statist. 24 (6) (1996) 2350-2383.
7. L. Breiman, P. Spector, Submodel selection and evaluation in regression: the x-random case, Int. Statist. Rev. 60 (3) (1992) 391-419.
8. Th. Buzug, G. Pfister, Comparison of algorithms calculating optimal embedding parameters for delay time coordinates, Physica D 58 (1992) 127-137.
9. L. Cao, Practical method for determining the minimum embedding dimension of a scalar time series, Physica D 110 (1997) 43-50.
10. M. Casdagli, Nonlinear prediction of chaotic time series, Physica D 35 (1989) 335-356.
11. M. Casdagli, D. Des Jardins, S. Eubank, J.D. Farmer, J. Gibson, J. Theiler, Nonlinear modeling of chaotic time series: theory and applications, in: Jong Hyun Kim, J. Stringer (Eds.), Applied Chaos, Wiley, New York, 1992, pp. 335-380.
12. M.C. Casdagli, A.S. Weigend, Exploring the continuum between deterministic and stochastic modeling, in: A.S. Weigend, N.A. Gershenfeld (Eds.), Time Series Prediction, Santa Fe Institute Studies in the Sciences of Complexity, Addison-Wesley, Reading, MA, 1994, pp. 347-366.
13. J.D. Farmer, J.J. Sidorowich, Exploiting chaos to predict the future and reduce noise, in: Yee Chung Lee (Ed.), Evolution, Learning and Cognition, World Scientific, Singapore, 1988, pp. 277-330.
14. J.D. Farmer, J.J. Sidorowich, Predicting chaotic time series, Phys. Rev. Lett. 59 (8) (1987) 845-848.
15. K. Fraedrich, B. Rückert, Metric adaption for analog forecasting, Physica A 253 (1998) 379-393.
16. J.H. Friedman, J.L. Bentley, R.A. Finkel, An algorithm for finding best matches in logarithmic expected time, ACM Trans. Math. Software 3 (3) (1977) 209-226.
17. P. García, J. Jiménez, A. Marcano, F. Moleiro, Local optimal metrics and nonlinear modeling of chaotic time series, Phys. Rev. Lett. 76 (9) (1966) 1449-1452.
18. C. Goutte, J. Larsen, Adaptive metric kernel regression, J. VLSI Signal Process. 26 (2000) 155-167.
19. T. Hastie, R. Tibshirani, Discriminant adaptive nearest neighbor classification, IEEE Trans. Pattern Anal. Mach. Intell. 18 (6) (1996) 607-616.
20. I. Katsavounidis, C.-C. Jay Kuo, Z. Zhang, Fast tree-structured nearest neighbor encoding for vector quantization, IEEE Trans. Image Process. 5 (2) (1996) 398-404.
21. D. Kugiumtzis, State space reconstruction parameters in the analysis of chaotic time series - the role of the time window length, Physica D 95 (1996) 13-28.
22. D. Kugiumtzis, Assessing different norms in nonlinear analysis of noisy time series, Physica D 105 (1997) 62-78.
23. D.G. Lowe, Similarity metric learning for a variable-kernel classifier, Neural Comput. 7 (1) (1995) 72-85.
24. D.G. Luenberger, Linear and Nonlinear Programming, 2nd Edition, Addison-Wesley, Reading, MA, 1984.
25. J. McNames, A nearest trajectory strategy for time series prediction, in: Proceedings of the International Workshop on Advanced Black-Box Techniques for Nonlinear Modeling, Katholieke Universiteit Leuven, Belgium, July 1998, pp. 112-128.
26. J. McNames, Innovations in local modeling for time series prediction, Ph.D. Thesis, Stanford University, 1999.
27. J. McNames, J. Suykens, J. Vandewalle, Winning entry of the K.U. Leuven time-series prediction competition, Int. J. Bifurcation Chaos 9 (8) (1999) 1485-1500.
28. D.B. Murray, Forecasting a chaotic time series using an improved metric for embedding space, Physica D 68 (1993) 318-325.
29. T. Sauer, J.A. Yorke, M. Casdagli, Embedology, J. Statist. Phys. 65 (3) (1991) 579-616.
30. S. Schaal, C.G. Atkeson, Constructive incremental learning from only local information, Neural Comput. 10 (8) (1998) 2047-2084.
31. L.A. Smith, Local optimal prediction: exploiting strangeness and the variation of sensitivity to initial condition, Philos. Trans. Roy. Soc. A 348 (1994) 371-381.
32. F. Takens, Detecting strange attractors in turbulence, in: D.A. Rand, L.S. Young (Eds.), Dynamical Systems and Turbulence, Lecture Notes in Mathematics, Vol. 898, Springer, Berlin, 1981, pp. 336-381.
33. N. Tanaka, H. Okamoto, M. Naito, An optimal metric for predicting chaotic time series, Jpn. J. Appl. Phys. 34 (1) (1995) 388-394.
34. P.J. Werbos, Backpropagation through time: what it does and how to do it, Proc. IEEE 78 (10) (1990) 1550-1560.
35. R.J. Williams, D. Zipser, A learning algorithm for continually running fully recurrent neural networks, Neural Comput. 1 (2) (1989) 270-280.