Research Article
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Comparison of the Global, Local and Semi-Local Chaotic Prediction Methods for Stock Markets: The Case of FTSE-100 Index

Year 2019, Volume: 7 Issue: 2, 289 - 300, 31.12.2019

Ayşe İşi Fatih Çemrek

https://doi.org/10.17093/alphanumeric.629722

Abstract

Chaotic prediction methods are classified as global, local and semi-local methods. In this paper, unlike the studies in the literature, it is aimed to compare all these methods together for stock markets in terms of prediction performance and to determine the best prediction method for stock markets. For this purpose, Multi-Layer Perceptron (MLP) neural networks from global methods, nearest neighbour method from local methods, radial basis functions from semi-local methods are used. The FTSE-100 index is selected to represent the stock market and applied the all methods to these data. The prediction performance is measured in term of root mean square error (RMSE) and normalized mean square error (NMSE). As a result of the analysis; it has been determined that the best prediction method for the FTSE-100 index is the semi-local method. While it is possible to make a maximum of 5 days prediction with global and local methods, it has been determined that up to 20 days prediction can be made with the semi-local prediction methods. The results show that semi-local prediction methods are successful in predicting the behaviour of stock market.

Keywords

Chaotic time series chaotic prediction Nearest Neighbor Method Radial Basis Functions Method Stock Market FTSE-100 Index

Supporting Institution

Eskişehir Osmangazi Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

2016-1178

Thanks

This study was supported by the Scientific Research Project Unit of Eskisehir Osmangazi University (Project number: 2016-1178).

References

  • Abarbanel, H. (1996). Analysis Of Observed Chaotic Data. New York: Spinger-Verlag.
  • Abarbanel, H. D., Brown, R., Kadtke, J. B. (1990). “Prediction in chaotic nonlinear systems: methods for time series with broadband fourier spectra”. Physical Review A, 41(4), 1782-1807.
  • Abhyankar, A., Copeland, L. S., Wong, W. (1995). “Nonlinear dynamics in real-time equity market indices: evidence from the United Kingdom”. The Economic Journal, 864-880.
  • Abhyankar, A., Copeland, L. S., Wong, W. (1997). “Uncovering nonlinear structure in real-time stock-market indexes: The S&P 500, the DAX, the NIKKEI 225 and the FTSE 100”. Journal of Business and Economic Statistics, 15(1), 1-14.
  • Aihara, K., Takabe, T., Toyoda, M. (1990). Chaotic neural networks”. Physics Letters A, 144(6-7), 333-340.
  • Brock, W. A., Hsieh, D. A., Lebaron, B. D. (1991). Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. MIT Press.Cao, L. (1997). “Practical method for determining the minimum embedding dimension of a scalar time series”. Physica D: Nonlinear Phenomena, 110(1-2), 43-50.
  • Casdagli, M. (1992). “Chaos and deterministic versus stochastic non-linear modelling”. Journal of The Royal Statistical Society, Series B (Methodological), 54(2), 303-328.
  • Casdagli, M. (1989). “Nonlinear prediction of chaotic time series”. Physica D: Nonlinear Phenomena, 35(3), 335-356.
  • Chan, K.S., Tong, H. (2001). Chaos: A Statistical Perspective, New York: Springer-Verlag.
  • Crutchfield, J.P. And Mcnamara, B.S. (1987). “Equations of motion from a data series”. Complex Systems, 1, 417-452.
  • Duarte, F. B., Tenreiro Machado, J. A., Monteiro Duarte, G. (2010). “Dynamics of the DOW JONES and the NASDAQ stock indexes”. Nonlinear Dynamics, 61(4), 691-705.
  • Eckmann, J. P., Ruelle, D. (1985). “Ergodic theory of chaos and strange attractors”. Reviews of Modern Physics, 57(3), 617-656.
  • Eldridge, R. M., Coleman, M. P. (1993). “The British FTSE-100 Index: Chaotically Deterministic or Random”. Working Paper, School of Business, Fairfield University.Elshorbagy, A., Simonovic, S. P., Panu, U. S. (2002). “Estimation of missing streamflow data using principles of chaos theory”. Journal of Hydrology, 255(1), 123-133.
  • Elsner, J.B. (1992). “Predicting time series using a neural network as a method of distinguishing chaos from noise”. Journal of Physics A: Mathematical and General, 25(4) 843–850.
  • Farmer, J.D., Sidorowich, J.J. (1987). “Predicting chaotic time series”. Physical Review Letters, 59(8), 845-848.
  • Fraedrich, K. (1986). “Estimating the dimensions of weather and climate attractors”. Journal of The Atmospheric Sciences, 43(5), 419-432.
  • Fraser, A. M., Swinney, H. L. (1986). “Independent coordinates for strange attractors from mutual information”. Physical Reviews A, 33, 1134-1140.
  • Gkana, A., Zachilas, L. (2015). “Sunspot numbers: data analysis, predictions and economic impacts”. Journal Of Engineering Science And Technology Review, 8 (1), 79-85.
  • Grassberger, P., Procaccia, I. (1983a). “Characterization of strange attractors”. Physical Review Letters, 50(5), 346-349.
  • Grassberger, P., Procaccia, I. (1983b). “Measuring the strangeness of strange attractors”. Physica D: Nonlinear Phenomena, 9(1-2), 189-208.
  • Guegan, D., Mercier, L. (2005). “Prediction in chaotic time series: methods and comparisons with an application to financial intra-day data”. The European Journal Of Finance, 11(2), 137-150.
  • Hanias M., Magafas L., Konstantaki P. (2013). “Nonlinear analysis of S&P index”. Equilibrium Quarterly Journal of Economics and Economic Policy, 8(4), 125-135.
  • Hsieh, D.A. (1991). “Chaos and nonlinear dynamics: Application to financial markets”. Journal of Finance, 46(5), 1839–1877.
  • Huanga, W., Nakamoria, Y., Wangb, S. (2005). “Forecasting stock market movement direction with support vector machine”. Computers and Operations Research, 32(10), 2513–2522.
  • Kantz, H. (1994). “A robust method to estimate the maximal Lyapunov exponent of a time series”. Physics Letters A, 185(1), 77-87.
  • Kantz, H., Schreiber, T. (2004). Nonlinear Time Series Analysis. UK: Cambridge University Press.
  • Karunasinghe, D.S., Liong, S.Y. (2006). “Chaotic time series prediction with a global model: artificial neural network”. Journal of Hydrology, 323(1), 92-105.
  • Kennel, M.B., Brown, R., Abarbanel, H.D.I. (1992). “Determining embedding dimension for phase-space reconstruction using a geometrical construction”. Physical Review A, 45(6), 3403-3411.
  • Lapedes, A., Farber, R., (1987). Nonlinear Signal Processing Using Neural Networks: Prediction and System Modelling. Technical Report, Los Alamos National Laboratory, Los Alamos, NM.
  • Lillekjendlie, B., Kugiumtzis, D., Christophersen, N. (1994). “Chaotic time series part II: System identification and prediction”. Modeling, Identification And Control, 15, 225-243.
  • Mayfield, E. S., Mizrach, B. (1992). “On determining the dimension of real-time stock-price data”. Journal of Business and Economic Statistics, 10(3), 367-374.
  • Rosenstein, M. T., Collins, J. J., De Luca, C. J. (1993). “A practical method for calculating largest lyapunov exponents from small data sets”. Physica D: Nonlinear Phenomena, 65(1-2), 117-134.
  • Shang, P., Li, X., Kamae, S. (2005). “Chaotic analysis of traffic time series”. Chaos, Solitons and Fractals, 25(1), 121-128.
  • Sivakumar, B., Jayawardena, A. W., Fernando, T. M. K. G. (2002). “River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches”. Journal of Hydrology, 265(1), 225-245.
  • Smaoui, N. (1999). “An artificial neural network noise reduction method for chaotic attractors”. International Journal of Computer Mathematics, 73(4), 417-431.
  • Sprott, J. C. (2003). Chaos and Time Series Analysis. Oxford Press.
  • Sprott, J. C. (2010). Elegant Chaos: Algebraically Simple Chaotic Flows. World Scientific.
  • Su, L., Li, C. (2015). “Local prediction of chaotic time series based on polynomial coefficient autoregressive model”. Mathematical Problems in Engineering, 2015,.1-14.
  • Vaidyanathan, R., Krehbiel, T. (1992). “Does the S&P 500 futures mispricing series exhibit nonlinear dependence across time?”. Journal of Futures Markets, 12(6), 659-677.
  • Webel, K. (2012). “Chaos in German stock returns-new evidence from the 0–1 test”. Economics Letters, 115(3), 487-489.
  • Wolf, A., Swift, J. B., Swinney, H. L., Vastano, J. A. (1985). “Determining Lyapunov exponents from a time series”. Physica D: Nonlinear Phenomena,16(3), 285-317.
  • Xiaofeng, G., Lai, C. H. (1999). “Improvement of the local prediction of chaotic time series”. Physical Review E, 60(5), 5463-5468.

Year 2019, Volume: 7 Issue: 2, 289 - 300, 31.12.2019

Ayşe İşi Fatih Çemrek

https://doi.org/10.17093/alphanumeric.629722

Abstract

Project Number

2016-1178

References

  • Abarbanel, H. (1996). Analysis Of Observed Chaotic Data. New York: Spinger-Verlag.
  • Abarbanel, H. D., Brown, R., Kadtke, J. B. (1990). “Prediction in chaotic nonlinear systems: methods for time series with broadband fourier spectra”. Physical Review A, 41(4), 1782-1807.
  • Abhyankar, A., Copeland, L. S., Wong, W. (1995). “Nonlinear dynamics in real-time equity market indices: evidence from the United Kingdom”. The Economic Journal, 864-880.
  • Abhyankar, A., Copeland, L. S., Wong, W. (1997). “Uncovering nonlinear structure in real-time stock-market indexes: The S&P 500, the DAX, the NIKKEI 225 and the FTSE 100”. Journal of Business and Economic Statistics, 15(1), 1-14.
  • Aihara, K., Takabe, T., Toyoda, M. (1990). Chaotic neural networks”. Physics Letters A, 144(6-7), 333-340.
  • Brock, W. A., Hsieh, D. A., Lebaron, B. D. (1991). Nonlinear Dynamics, Chaos and Instability: Statistical Theory and Economic Evidence. MIT Press.Cao, L. (1997). “Practical method for determining the minimum embedding dimension of a scalar time series”. Physica D: Nonlinear Phenomena, 110(1-2), 43-50.
  • Casdagli, M. (1992). “Chaos and deterministic versus stochastic non-linear modelling”. Journal of The Royal Statistical Society, Series B (Methodological), 54(2), 303-328.
  • Casdagli, M. (1989). “Nonlinear prediction of chaotic time series”. Physica D: Nonlinear Phenomena, 35(3), 335-356.
  • Chan, K.S., Tong, H. (2001). Chaos: A Statistical Perspective, New York: Springer-Verlag.
  • Crutchfield, J.P. And Mcnamara, B.S. (1987). “Equations of motion from a data series”. Complex Systems, 1, 417-452.
  • Duarte, F. B., Tenreiro Machado, J. A., Monteiro Duarte, G. (2010). “Dynamics of the DOW JONES and the NASDAQ stock indexes”. Nonlinear Dynamics, 61(4), 691-705.
  • Eckmann, J. P., Ruelle, D. (1985). “Ergodic theory of chaos and strange attractors”. Reviews of Modern Physics, 57(3), 617-656.
  • Eldridge, R. M., Coleman, M. P. (1993). “The British FTSE-100 Index: Chaotically Deterministic or Random”. Working Paper, School of Business, Fairfield University.Elshorbagy, A., Simonovic, S. P., Panu, U. S. (2002). “Estimation of missing streamflow data using principles of chaos theory”. Journal of Hydrology, 255(1), 123-133.
  • Elsner, J.B. (1992). “Predicting time series using a neural network as a method of distinguishing chaos from noise”. Journal of Physics A: Mathematical and General, 25(4) 843–850.
  • Farmer, J.D., Sidorowich, J.J. (1987). “Predicting chaotic time series”. Physical Review Letters, 59(8), 845-848.
  • Fraedrich, K. (1986). “Estimating the dimensions of weather and climate attractors”. Journal of The Atmospheric Sciences, 43(5), 419-432.
  • Fraser, A. M., Swinney, H. L. (1986). “Independent coordinates for strange attractors from mutual information”. Physical Reviews A, 33, 1134-1140.
  • Gkana, A., Zachilas, L. (2015). “Sunspot numbers: data analysis, predictions and economic impacts”. Journal Of Engineering Science And Technology Review, 8 (1), 79-85.
  • Grassberger, P., Procaccia, I. (1983a). “Characterization of strange attractors”. Physical Review Letters, 50(5), 346-349.
  • Grassberger, P., Procaccia, I. (1983b). “Measuring the strangeness of strange attractors”. Physica D: Nonlinear Phenomena, 9(1-2), 189-208.
  • Guegan, D., Mercier, L. (2005). “Prediction in chaotic time series: methods and comparisons with an application to financial intra-day data”. The European Journal Of Finance, 11(2), 137-150.
  • Hanias M., Magafas L., Konstantaki P. (2013). “Nonlinear analysis of S&P index”. Equilibrium Quarterly Journal of Economics and Economic Policy, 8(4), 125-135.
  • Hsieh, D.A. (1991). “Chaos and nonlinear dynamics: Application to financial markets”. Journal of Finance, 46(5), 1839–1877.
  • Huanga, W., Nakamoria, Y., Wangb, S. (2005). “Forecasting stock market movement direction with support vector machine”. Computers and Operations Research, 32(10), 2513–2522.
  • Kantz, H. (1994). “A robust method to estimate the maximal Lyapunov exponent of a time series”. Physics Letters A, 185(1), 77-87.
  • Kantz, H., Schreiber, T. (2004). Nonlinear Time Series Analysis. UK: Cambridge University Press.
  • Karunasinghe, D.S., Liong, S.Y. (2006). “Chaotic time series prediction with a global model: artificial neural network”. Journal of Hydrology, 323(1), 92-105.
  • Kennel, M.B., Brown, R., Abarbanel, H.D.I. (1992). “Determining embedding dimension for phase-space reconstruction using a geometrical construction”. Physical Review A, 45(6), 3403-3411.
  • Lapedes, A., Farber, R., (1987). Nonlinear Signal Processing Using Neural Networks: Prediction and System Modelling. Technical Report, Los Alamos National Laboratory, Los Alamos, NM.
  • Lillekjendlie, B., Kugiumtzis, D., Christophersen, N. (1994). “Chaotic time series part II: System identification and prediction”. Modeling, Identification And Control, 15, 225-243.
  • Mayfield, E. S., Mizrach, B. (1992). “On determining the dimension of real-time stock-price data”. Journal of Business and Economic Statistics, 10(3), 367-374.
  • Rosenstein, M. T., Collins, J. J., De Luca, C. J. (1993). “A practical method for calculating largest lyapunov exponents from small data sets”. Physica D: Nonlinear Phenomena, 65(1-2), 117-134.
  • Shang, P., Li, X., Kamae, S. (2005). “Chaotic analysis of traffic time series”. Chaos, Solitons and Fractals, 25(1), 121-128.
  • Sivakumar, B., Jayawardena, A. W., Fernando, T. M. K. G. (2002). “River flow forecasting: use of phase-space reconstruction and artificial neural networks approaches”. Journal of Hydrology, 265(1), 225-245.
  • Smaoui, N. (1999). “An artificial neural network noise reduction method for chaotic attractors”. International Journal of Computer Mathematics, 73(4), 417-431.
  • Sprott, J. C. (2003). Chaos and Time Series Analysis. Oxford Press.
  • Sprott, J. C. (2010). Elegant Chaos: Algebraically Simple Chaotic Flows. World Scientific.
  • Su, L., Li, C. (2015). “Local prediction of chaotic time series based on polynomial coefficient autoregressive model”. Mathematical Problems in Engineering, 2015,.1-14.
  • Vaidyanathan, R., Krehbiel, T. (1992). “Does the S&P 500 futures mispricing series exhibit nonlinear dependence across time?”. Journal of Futures Markets, 12(6), 659-677.
  • Webel, K. (2012). “Chaos in German stock returns-new evidence from the 0–1 test”. Economics Letters, 115(3), 487-489.
  • Wolf, A., Swift, J. B., Swinney, H. L., Vastano, J. A. (1985). “Determining Lyapunov exponents from a time series”. Physica D: Nonlinear Phenomena,16(3), 285-317.
  • Xiaofeng, G., Lai, C. H. (1999). “Improvement of the local prediction of chaotic time series”. Physical Review E, 60(5), 5463-5468.
There are 42 citations in total.

Details

Primary Language English
Subjects Operation
Journal Section Articles
Authors

Ayşe İşi 0000-0002-9944-1038

Fatih Çemrek This is me 0000-0002-6528-7159

Project Number 2016-1178
Publication Date December 31, 2019
Submission Date August 5, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA İşi, A., & Çemrek, F. (2019). Comparison of the Global, Local and Semi-Local Chaotic Prediction Methods for Stock Markets: The Case of FTSE-100 Index. Alphanumeric Journal, 7(2), 289-300. https://doi.org/10.17093/alphanumeric.629722
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