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Economics
Financial Economics

Can we predict the unpredictable?

Profile image of Robin GrasRobin Gras

2014, Scientific Reports

https://doi.org/10.1038/SREP06834
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6 pages

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Abstract

Time series forecasting is of fundamental importance for a variety of domains including the prediction of earthquakes, financial market prediction, and the prediction of epileptic seizures. We present an original approach that brings a novel perspective to the field of long-term time series forecasting. Nonlinear properties of a time series are evaluated and used for long-term predictions. We used financial time series, medical time series and climate time series to evaluate our method. The results we obtained show that the long-term prediction of complex nonlinear time series is no longer unrealistic. The new method has the ability to predict the long-term evolutionary trend of stock market time series, and it attained an accuracy level with 100% sensitivity and specificity for the prediction of epileptic seizures up to 17 minutes in advance based on data from 21 epileptic patients. Our new method also predicted the trend of increasing global temperature in the last 30 years with a high level of accuracy. Thus, our method for making long-term time series predictions is vastly superior to existing methods. We therefore believe that our proposed method has the potential to be applied to many other domains to generate accurate and useful long-term predictions. T he prediction of future values in a complex time series is a major interest for scientists , with applications to various scientific fields . There are many natural phenomena that require a prediction algorithm for answering important questions, such as estimating future population variations, predicting the orbits of astronomical objects and predicting the occurrence of seismic waves. The prediction of twenty-first century global temperature rise would be a valuable resource for policy makers and planners 6 . Population projections may be used to predict species extinction before they reach a crisis point 5 . Moreover, prediction is an ongoing and pressing problem in the forecasting of economic time series 8 . In the medical sciences, there are also many applications for which an efficient prediction algorithm could save lives. A large number of time series obtained from monitoring the human body can be used as a basis for the decision-making process to treat or prevent grave diseases such as epilepsy or Alzheimer's disease . It has been shown that data generated by such natural phenomena often behave chaotically 11 . Although chaotic behaviours are deterministic, their complex properties make it difficult to distinguish them from random behaviour. Chaotic behaviours are known to be strongly dependent on initial conditions; small changes in initial conditions can possibly lead to immense changes in subsequent time steps and are particularly difficult to predict. Because the exact conditions for many natural phenomena are not known and the properties of a chaotic time series are very complex, it is difficult to model these systems. Most of the existing methods for complex time series prediction are based on modelling the time series to predict future values, although there are other types of methods such as agent-based simulations that model the system generating the time series 21 . Model-based approaches can be classified into two main domains: linear modelling such as in ARIMA (autoregressive integrated moving average) and nonlinear modelling such as in MLP (multi-layer perceptron) and GARCH (generalised autoregressive conditional heteroskedasticity) (for details, see Supplementary Information, section 1). However, other studies have concluded that there is no clear evidence in favour of nonlinear models over linear models in terms of forecasting performance 7 . Regardless, there is no robust procedure that can produce an accurate model for chaotic time series. For all of these methods, the prediction error increases dramatically with the number of time points predicted . Therefore, most of the existing methods focus on very short-term predictions to obtain a reasonable level of accuracy. None of the existing methods demonstrate an acceptable level of accuracy for long-term prediction 12 . For example, for financial time series predictions, most methods can predict only one step ahead, which is not very helpful for acting against a financial crisis before it occurs . To address this deficiency in existing methods, we propose a novel approach to making long-term time series predictions (see Methods), GenericPred 24 , with applications to financial time series, medical diagnosis and global temperature prediction.

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References (39)

  1. Lehnertz, K. & Elger, C. E. Can epileptic seizures be predicted? evidence from nonlinear time series analyses of brain electrical activity. Phys. Rev. Lett. 80, 5019-5023 (1998).
  2. Jeong, J. Nonlinear dynamics of EEG in Alzheimer's disease. Drug. Dev. Res. 56, 57-66 (2002).
  3. Dauwels, J., Vialatte, F., Latchoumane, C., Jeong, J. & Cichocki, A. EEG synchrony analysis for early diagnosis of Alzheimer's disease: a study with several synchrony measures and EEG data sets. Paper presented at Engineering in Medicine and Biology Society, Minneapolis. US-New York: IEEE, 2224-2227 (2009 Sep).
  4. Newman, W. I., Gabrielov, A. M. & Turcotte, D. L. Nonlinear Dynamics and Predictability of Geophysical Phenomena [Newman, W. I., Gabrielov, A. M. & Turcotte, D. L. (ed.)][15-35] (American Geophysical Union, Washington, 1994).
  5. Sugihara, G. et al. Detecting causality in complex ecosystems. Science 338, 496-500 (2012).
  6. Stott, Peter, A. & Kettleborough, J. A. Origins and estimates of uncertainty in predictions of twenty-first century temperature rise. Nature 416, 723-726 (2002).
  7. Clements, M. P., Franses, P. H. & Swanson, N. R. Forecasting economic and financial time-series with non-linear models. Int. J. Forecast. 20, 169-183 (2004).
  8. Arrow, K. J. et al. The promise of prediction markets. Science 320, 877-878 (2008).
  9. Zhang, G. P. & Kline, D. Quarterly time-series forecasting with neural networks. IEEE. Trans. Neural. Netw. 18, 1800-1814 (2007).
  10. Gooijer, J. D. D. & Hyndman, R. 25 Years of time series forecasting. Int. J. Forecast. 22, 442-473 (2006).
  11. Romanelli, L., Figliola, M. A. & Hirsch, F. A. Deterministic chaos and natural phenomena. J. Stat. Phys. 53, 991-994 (1988).
  12. Zanin, M. Forbidden patterns in financial time series. Chaos 18, 013119 (2008).
  13. Boettiger, C. & Hastings, A. Tipping points: From patterns to predictions. Nature 493, 157-158 (2013).
  14. Scheffer, M. Complex systems: Foreseeing tipping points. Nature 467, 411-412 (2010).
  15. Podobnik, B. et al. Network Risk and Forecasting Power in Phase-Flipping Dynamical Networks. Phys. Rev. E 89, 042807 (2014).
  16. Drake, J. M. & Griffen, B. D. Early warning signals of extinction in deteriorating environments. Nature 467, 456-459 (2010).
  17. Becks, L., Hilker, F. M., Malchow, H., Jurgens, K. & Arndt, H. Experimental demonstration of chaos in a microbial food web. Nature 435, 1226-1229 (2005).
  18. Box, G. E. P., Jenkins, G. M. & Reinsel, G. C. Time Series Analysis: Forecasting and Control (Prentice-Hall, Englewood Cliffs, 1994).
  19. Montgomery, D. C., Johnson, L. A. & Gardiner, J. S. Forecasting and Time Series Analysis (McGraw Hill, New York, 1990).
  20. Gottman, J. M. Time Series Analysis (Cambridge University Press, Cambridge, 1981).
  21. Neri, F. Learning and predicting financial time series by combining natural computation and agent simulation. EvoApplications 6625, 111-119 (2011).
  22. Zirilli, J. S. Financial prediction using Neural Networks (International Thompson Computer Press, London, 1997).
  23. Bollerslev, T. Generalized autoregressive conditional heteroskedasticity. J. Econometrics. 31,307-327 (1986).
  24. Filed under US Patent Application Serial Number 61/882863 (granted Sep. 26 2013).
  25. Golestani, A., Jahed Motlagh, M. R., Ahmadian, K., Omidvarnia, A. H. & Mozayani, N. A new criterion for distinguish stochastic and deterministic time series with the Poincare ´section and fractal dimension, Chaos 19, 013137 (2009).
  26. Shouyi, W., Chaovalitwongse, W. A. & Wong, S. Online seizure prediction using an adaptive learning approach, IEEE Trans. Knowledge Data Eng. 25, 2854-2866 (2013).
  27. Seneviratne, S. I., Donat, M. G., Mueller, B. & Alexander, L. V. No pause in the increase of hot temperature extremes. Nature Clim. Change. 4, 161-163 (2014).
  28. Smith, D. M. et al. Improved surface temperature prediction for the coming decade from a global climate model. Science 317, 796-799 (2007).
  29. Hahn, R. & Tetlock, P. Using information markets to improve public decision making. J. Law Pub. Pol. 28, 213 (2005).
  30. Lu ¨tkepohl, H. New Introduction to Multiple Time Series Analysis (Springer- Verlag, Berlin, 2005).
  31. Meinardi, H., Scott, R. A. & Reis, R. The treatment gap in epilepsy: the current situation and ways forward. Epilepsia 42, 136-149 (2001).
  32. Fisher, R. S., Boas, W. V. E., Blume, W., Elger, C. & Genton, P. Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE). Epilepsia 46, 470-472 (2005).
  33. Jirsa, V. K., Stacey, W. C., Quilichini, P. P., Ivanov, A. I. & Bernard, C. On the nature of seizure dynamics. Brain, awu133 (2014).
  34. Park, Y., Luo, L., Parhi, K. K. & Netoff, T. Seizure prediction with spectral power of EEG using cost-sensitive support vector machines. Epilepsia 52, 1761-1770 (2011).
  35. Feldwisch-Drentrup, H. et al. Joining the benefits: Combining epileptic seizure prediction methods. Epilepsia 51, 1598-1606 (2010).
  36. Ye, L. M., Yang, G. X., Van Ranst, E. & Tang, H. J. Time-series modeling and prediction of global monthly absolute temperature for environmental decision making. Adv. Atmos. Sci. 30, 382-396 (2013).
  37. Falconer, K. Fractal Geometry: Mathematical Foundations and Applications (Wiley, New York, 2007).
  38. Rosenstein, M. T., Collins, J. J. & De Luca, C. J. A practical method for calculating largest Lyapunov exponents from small data sets. Phys. D. 65,117-134 (1993).
  39. Golestani, A. & Gras, R. Regularity analysis of an individual-based ecosystem simulation. Chaos 20, 043120 (2010).

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