A tight upper bound on the gain of linear and nonlinear predictors for stationary stochastic processes

IEEE Transactions on Signal Processing

Volumn 46, Issue 11, 1998, Pages 2888-2897

  Bernhard, Hans Peter ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Chaos theory; Information theory; Load forecasting; Model selection; Mutual information; Mutual information function; Nonlinear predictors; Prediction

Indexed keywords

EID: 33747740736     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.726803     Document Type: Article

References (30)

1. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series. Cambridge, MA: MIT Press, 1949.
2. G. E. P. Box and G. M. Jenkins, Time Series Analysis. Forecasting and Control. San Francisco, CA: Holden-Day, 1976.
3. J. Rissanen, "Universal coding, information, prediction, and estimation," IEEE Trans. Inform. Theory, vol. IT-30, pp. 629-636, July 1984.
4. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall, 1993.
5. L. L. Scharf, Statistical Signal Processing. Reading, MA: Addison Wesley, 1991.
6. A. Lapedes and R. Farber, "How neural nets work," in Evolution, Learning, and Cognition, Y. C. Lee, Ed. Singapore: World Scientific, 1988, pp. 231-346.
7. S. Haykin, Neural Networks: A Comprehensive Foundation. New York: Macmillan, 1994.
8. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
9. G. Grimmett and D. Welsh, Probability: An Introduction. Oxford, U.K.: Clarendon, 1991.
10. H.-P. Bernhard, "The mutual information function and its application to signal processing," Ph.D. dissertation, Tech. Universität Wien, Vienna, Austria, 1997.
11. A. M. Fraser and H. L. Swinney, "Independent coordinates for strange attractors from mutual information," Phys. Rev. A, vol. 33, no. 2, pp. 1134-1140, Feb. 1986.
12. A. M. Fraser, "Information and entropy in strange attractors," IEEE Trans. Inform. Theory, vol. 35, pp. 245-262, Mar. 1989.
13. M. Palus, V. Albrecht, and I. Dvorak, "Information-theoretic test for nonlinearity in time series," Phys. Lett., vol. A, no. 175, 1993.
14. M. Palus, "Testing for nonlinearity using redundancies," Physica D, vol. 80, pp. 335-345, 1995.
15. N. S. Jayant and P. Noll, Digital Coding of Waveforms-Principles and Applications to Speech and Video. Englewood Cliffs, NJ: Prentice-Hall, 1984.
16. M. B. Kennel, "The multiple-dimensions mutual information program," Preprint. Available WWW from lyapunov.ucsd.edu, 1993.
17. G. R. Terrel and D. W. Scott, "Variable kernel density estimation," Ann. Statist., 1992.
18. H.-P. Bernhard and G. Kubin, "A fast mutual information calculation algorithm," in Signal Processing VII: Theories and Applications, M. J. J. Holt, C. F. N. Cowan, P. M. Grant, and W. A. Sandham, Eds. Amsterdam, The Netherlands: Elsevier, Sept. 1994, pp. 50-53, vol. 1.
19. S. Fröhlich, "Numerische Berechnung der Transinformation von Zeitrei-hen (numerical calculation of the mutual information of time series)," Diploma Thesis, Technische Univ. Wien, Vienna, Austria, 1996.
20. R. L. Dobrushin, "General formulation of Shannon's main theorem in information theory," Amer. Math. Soc. Trans., vol. 33, pp. 323138, 1959.
21. B. Pompe, "Ranking and entropy estimation in nonlinear time series analysis," in Nonlinear Techniques in Physiological Time Series Analy-sis, H. Kantz, J. Kurths, and G. Mayer-Kress, Eds. Berlin, Germany: Springer, 1996.
22. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. Tokyo, Japan, New York: McGraw-Hill, 1984.
23. R. Gencay and W. D. Dechert, "An algorithm for the n Lyapunov exponents of a ra-dimensional unknown dynamical system," Physica D, vol. 59, pp. 142-157, 1992.
24. R. Shaw, "Strange attractors, chaotic behavior, and information flow," Zeitschrift für Naturforschung, vol. 36a, pp. 80-112, 1981.
25. B. Knapp, H. Strasser, K. Yurtsever, and H.-P. Bernhard, "Chaostheoretic methods for load forecasting in the field of energy management systems," in Proc. Power Syst. Comput. Conf., Dresden, Germany, 1996.
26. G. Gross and F. D. Galiana, "Short-term load forecasting," in Proc. Conf. IEEE, Montreal, P.Q., Canada, Dec. 1987, pp. 1558-1573.
27. T. Baumann, E. Thurner, and D. Deisenhofer, "Real world implementation of a short-term load forecasting method using modular neural networks," in Proc. 12th Power Syst. Comput. Conf., Dresden, Germany, 1996.
28. A. Khotanzad et al., "Annstlf-A neural-network-based electric load forecasting system," IEEE Trans. Neural Networks, vol. 8, pp. 835-846, July 1997.
29. H.-P. Bernhard, "Anwendung Informationstheoretischer Methoden in der Signalverarbeitung am Beispiel der Lastkurvenanalyse (application of information theoretic methods in signal processing for the example of load curves)," Elektrotechnik und Informationstechnik, pp. 3310, Jan. 1998.
30. W. Reinisch, "Transinformationsanalyse von Lastkurven (mutual information analysis of load curves)," Diploma Thesis, Technische Univ. Wien, Vienna, Austria, 1997.