Model-free Prediction based on Tracking Theory and Newton Form of Polynomial
The majority of existing predictors for time series are
model-dependent and therefore require some prior knowledge for the
identification of complex systems, usually involving system
identification, extensive training, or online adaptation in the case of
time-varying systems. Additionally, since a time series is usually
generated by complex processes such as the stock market or other
chaotic systems, identification, modeling or the online updating of
parameters can be problematic. In this paper a model-free predictor
(MFP) for a time series produced by an unknown nonlinear system or
process is derived using tracking theory. An identical derivation of the
MFP using the property of the Newton form of the interpolating
polynomial is also presented. The MFP is able to accurately predict
future values of a time series, is stable, has few tuning parameters and
is desirable for engineering applications due to its simplicity, fast
prediction speed and extremely low computational load. The
performance of the proposed MFP is demonstrated using the
prediction of the Dow Jones Industrial Average stock index.
[1] D. J. Trudnowski, W.L. McReynolds, J.M.Johnson, "Real-time very
short-term load prediction for power-system automatic generation
control," IEEE Trans. Control Systems Technology vol 9 pp: 254 - 260,
2001.
[2] M. H. Ali, T. Murata, J. Tamura, "Influence of Communication Delay on
the Performance of Fuzzy Logic-Controlled Braking Resistor Against
Transient Stability," IEEE Trans Control System and Technology, vol
16, pp: 1232 - 1241, 2008.
[3] A.S. Sharma, D.J.N. Limebeer, I.M. Jaimoukha, J.B. Lister, "Modeling
and control of TCV", IEEE Trans. Control Systems Technology, vol 13,
pp: 356 -369, 2005
[4] B. L. Bowerman and R. T. O-Connell, Time Series Forecasting. New
York: PWS, 1987.
[5] J. T. Spooner, M. Maggiore, R. Ord├│├▒, and K. M. Passino, Adaptive
Control and Estimation for Nonlinear Systems: Neural and Fuzzy
Approximator Techniques. New York: Wiley, 2002.
[6] G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction, and Control.
Englewood Cliffs, NJ: Prentice-Hall, 1984.
[7] T. Matsumoto, Y. Nakajima, M. Saito, J. Sugi and H. Hamagishi,
"Reconstructions and predictions of nonlinear dynamical systems: a
hierarchical bayesian Aapproach," IEEE Trans. Signal Proc., vol. 49, pp.
2138 - 2155, 2001.
[8] A. M. González, A. M. S. Roque and J. García-González. "Modeling and
forecasting electricity prices with input/output hidden markov models,"
IEEE Trans. Power Syst., vol. 20, pp. 13- 24, 2005.
[9] V. J. Mathews, "Adaptive polynomial filters", IEEE Signal Processing,
vol. 8, pp. 10-26, 1991.
[10] J. T. Conner, R. D. Martin, and L. Atlas, "Recurrent neural networks and
robust time series prediction," IEEE Trans. Neural Networks., vol. 5, pp.
240-254, 1994.
[11] O. Ra├║l, T. J. Spooner and M. Kevin, "Passino. Experimental studies in
nonlinear discrete-time Adaptive prediction and control," IEEE Trans. on
Fuzzy Syst., vol. 14, pp. 275-286, 2006.
[12] C. V. Altrock, Fuzzy Logic & NeuroFuzzy Applications Explained,
Englewood Cliffs, NJ: Prentice Hall, 1995.
[13] V. Varadan, H. Leung, and ├ë. Bossé, "Dynamical model reconstruction
and accurate prediction of power-pool time series." IEEE Trans. Instru.
Measurement, vol. 55, pp. 327-336, 2006.
[14] S. F. Su, C. B. Lin and Y. T. Hsu, "A high precision global prediction
approach based on local prediction approaches." IEEE Trans. System Man
and Cybernetic ÔÇöPart C: Aplications and Reviews, vol. 32, pp. 416-525,
2002.
[15] G. Qi, Z. Chen and Z. Yuan, "Model free control of affine chaotic
system," Phys. Lett. A., vol. 344, pp. 189-202, 2005.
[16] [16] G. Qi, Z. Chen and Z. Yuan. "Adaptive high order differential
feedback control for affine nonlinear system," Chaos, Solitons &
Fractals, vol. 37, pp. 308-315, 2008.
[17] G. Qi, M.A. van Wyk and B. J. van Wyk, "Model-free differential states
observer for nonlinear affine system," The 7th International Federation of
Automation Control (IFAC) Symposium on Nonlinear Control systems,
pp. 984-989, 2007.
[18] G. Qi, Z. Chen, Z. Yuan, Stable high orders differentiator design and its
application in observer and controller. The Chinese Journal of
Electronics,vol. 14, pp. 644-648, 2005.
[19] F. Takens, Detecting strange attractors in turbulence, in: D. A. Rand, L. S.
Young (Eds.), Dynamical Systems and Turbulence, vol. 898, Springer,
Berlin, 365-381, 1981.
[20] M. B. Kennel, R. Brown, and H. D. I. "Abarbanel. Determining
embedding dimension for phase-space reconstruction using a geometrical
construction," Phys. Rev. A, Gen. Phys., vol. 45, pp. 3403-3411, 1992.
[21] F. Gustafsson, "Determining the initial states in forward-backward
filtering," IEEE Trans. Signal Processing, vol. 44, pp. 988ÔÇö992, 1996.
[22] S. K. Mitra, Digital Signal Processing, 2nd ed., McGraw-Hill, Sections
4.4.2 and 8.2.5. 2001.
[23] http://planetmath.org/encyclopedia/DividedDifference.html
[24] M. C. Mackey and L. Glass, "Oscillation and chaos in physiological
control systems," Science, vol. 197, pp. 287-289, 1977.
[25] J. Zhang, X. Xiao, Predicting hyper-chaotic time series using adaptive
higher-order nonlinear filter. Chin. Phys. Lett. vol. 18, pp. 337-340, 2001.
[26] V. J. Mathews, "Adaptive polynomial filters", IEEE Signal Processing,
vol. 8, pp. 10-26, 1991.
[27] F. Rauf and H. M. Ahmed, New Nonlinear Adaptive Filters with
Applications to Chaos, Int. J. Bifurcation Chaos, vol. 7, pp. 1791-1809,
1997
[1] D. J. Trudnowski, W.L. McReynolds, J.M.Johnson, "Real-time very
short-term load prediction for power-system automatic generation
control," IEEE Trans. Control Systems Technology vol 9 pp: 254 - 260,
2001.
[2] M. H. Ali, T. Murata, J. Tamura, "Influence of Communication Delay on
the Performance of Fuzzy Logic-Controlled Braking Resistor Against
Transient Stability," IEEE Trans Control System and Technology, vol
16, pp: 1232 - 1241, 2008.
[3] A.S. Sharma, D.J.N. Limebeer, I.M. Jaimoukha, J.B. Lister, "Modeling
and control of TCV", IEEE Trans. Control Systems Technology, vol 13,
pp: 356 -369, 2005
[4] B. L. Bowerman and R. T. O-Connell, Time Series Forecasting. New
York: PWS, 1987.
[5] J. T. Spooner, M. Maggiore, R. Ord├│├▒, and K. M. Passino, Adaptive
Control and Estimation for Nonlinear Systems: Neural and Fuzzy
Approximator Techniques. New York: Wiley, 2002.
[6] G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction, and Control.
Englewood Cliffs, NJ: Prentice-Hall, 1984.
[7] T. Matsumoto, Y. Nakajima, M. Saito, J. Sugi and H. Hamagishi,
"Reconstructions and predictions of nonlinear dynamical systems: a
hierarchical bayesian Aapproach," IEEE Trans. Signal Proc., vol. 49, pp.
2138 - 2155, 2001.
[8] A. M. González, A. M. S. Roque and J. García-González. "Modeling and
forecasting electricity prices with input/output hidden markov models,"
IEEE Trans. Power Syst., vol. 20, pp. 13- 24, 2005.
[9] V. J. Mathews, "Adaptive polynomial filters", IEEE Signal Processing,
vol. 8, pp. 10-26, 1991.
[10] J. T. Conner, R. D. Martin, and L. Atlas, "Recurrent neural networks and
robust time series prediction," IEEE Trans. Neural Networks., vol. 5, pp.
240-254, 1994.
[11] O. Ra├║l, T. J. Spooner and M. Kevin, "Passino. Experimental studies in
nonlinear discrete-time Adaptive prediction and control," IEEE Trans. on
Fuzzy Syst., vol. 14, pp. 275-286, 2006.
[12] C. V. Altrock, Fuzzy Logic & NeuroFuzzy Applications Explained,
Englewood Cliffs, NJ: Prentice Hall, 1995.
[13] V. Varadan, H. Leung, and ├ë. Bossé, "Dynamical model reconstruction
and accurate prediction of power-pool time series." IEEE Trans. Instru.
Measurement, vol. 55, pp. 327-336, 2006.
[14] S. F. Su, C. B. Lin and Y. T. Hsu, "A high precision global prediction
approach based on local prediction approaches." IEEE Trans. System Man
and Cybernetic ÔÇöPart C: Aplications and Reviews, vol. 32, pp. 416-525,
2002.
[15] G. Qi, Z. Chen and Z. Yuan, "Model free control of affine chaotic
system," Phys. Lett. A., vol. 344, pp. 189-202, 2005.
[16] [16] G. Qi, Z. Chen and Z. Yuan. "Adaptive high order differential
feedback control for affine nonlinear system," Chaos, Solitons &
Fractals, vol. 37, pp. 308-315, 2008.
[17] G. Qi, M.A. van Wyk and B. J. van Wyk, "Model-free differential states
observer for nonlinear affine system," The 7th International Federation of
Automation Control (IFAC) Symposium on Nonlinear Control systems,
pp. 984-989, 2007.
[18] G. Qi, Z. Chen, Z. Yuan, Stable high orders differentiator design and its
application in observer and controller. The Chinese Journal of
Electronics,vol. 14, pp. 644-648, 2005.
[19] F. Takens, Detecting strange attractors in turbulence, in: D. A. Rand, L. S.
Young (Eds.), Dynamical Systems and Turbulence, vol. 898, Springer,
Berlin, 365-381, 1981.
[20] M. B. Kennel, R. Brown, and H. D. I. "Abarbanel. Determining
embedding dimension for phase-space reconstruction using a geometrical
construction," Phys. Rev. A, Gen. Phys., vol. 45, pp. 3403-3411, 1992.
[21] F. Gustafsson, "Determining the initial states in forward-backward
filtering," IEEE Trans. Signal Processing, vol. 44, pp. 988ÔÇö992, 1996.
[22] S. K. Mitra, Digital Signal Processing, 2nd ed., McGraw-Hill, Sections
4.4.2 and 8.2.5. 2001.
[23] http://planetmath.org/encyclopedia/DividedDifference.html
[24] M. C. Mackey and L. Glass, "Oscillation and chaos in physiological
control systems," Science, vol. 197, pp. 287-289, 1977.
[25] J. Zhang, X. Xiao, Predicting hyper-chaotic time series using adaptive
higher-order nonlinear filter. Chin. Phys. Lett. vol. 18, pp. 337-340, 2001.
[26] V. J. Mathews, "Adaptive polynomial filters", IEEE Signal Processing,
vol. 8, pp. 10-26, 1991.
[27] F. Rauf and H. M. Ahmed, New Nonlinear Adaptive Filters with
Applications to Chaos, Int. J. Bifurcation Chaos, vol. 7, pp. 1791-1809,
1997
@article{"International Journal of Electrical, Electronic and Communication Sciences:50494", author = "Guoyuan Qi and Yskandar Hamam and Barend Jacobus van Wyk and Shengzhi Du", title = "Model-free Prediction based on Tracking Theory and Newton Form of Polynomial", abstract = "The majority of existing predictors for time series are
model-dependent and therefore require some prior knowledge for the
identification of complex systems, usually involving system
identification, extensive training, or online adaptation in the case of
time-varying systems. Additionally, since a time series is usually
generated by complex processes such as the stock market or other
chaotic systems, identification, modeling or the online updating of
parameters can be problematic. In this paper a model-free predictor
(MFP) for a time series produced by an unknown nonlinear system or
process is derived using tracking theory. An identical derivation of the
MFP using the property of the Newton form of the interpolating
polynomial is also presented. The MFP is able to accurately predict
future values of a time series, is stable, has few tuning parameters and
is desirable for engineering applications due to its simplicity, fast
prediction speed and extremely low computational load. The
performance of the proposed MFP is demonstrated using the
prediction of the Dow Jones Industrial Average stock index.", keywords = "Forecast, model-free predictor, prediction, time series", volume = "5", number = "7", pages = "783-8", }
