Skip to main content

Bootstrap Prediction Intervals for Nonlinear Time-Series

  • Conference paper
Intelligent Data Engineering and Automated Learning – IDEAL 2006 (IDEAL 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4224))

Abstract

To evaluate predictability of complex behavior produced from nonlinear dynamical systems, we often use normalized root mean square error, which is suitable to evaluate errors between true points and predicted points. However, it is also important to estimate prediction intervals, where the future point will be included. Although estimation of prediction intervals is conventionally realized by an ensemble prediction, we applied the bootstrap resampling scheme to evaluate prediction intervals of nonlinear time-series. By several numerical simulations, we show that the bootstrap method is effective to estimate prediction intervals for nonlinear time-series.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Lorenz, E.N.: Atmospheric predictability as revealed by naturally occurring analogues. J. Atmospheric Sciences 26, 636–646 (1969)

    Article  Google Scholar 

  • Sano, M., Sawada, Y.: Measurement of the lyapunov spectrum from a chaotic time series. Physical Review Letters 55(10), 1082–1085 (1985)

    Article  MathSciNet  Google Scholar 

  • Haraki, D., Suzuki, T., Ikeguchi, T.: Bootstrap Nonlinear Prediction. submitted to Physical Review E (2005)

    Google Scholar 

  • Lora, A.T., Santos, J.M.R., Riquelme, J.C., Expósito, A.G., Ramos, J.L.M.: Time-series prediction: Application to the short-term electric energy demand. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, J.-L. (eds.) CAEPIA/TTIA 2003. LNCS (LNAI), vol. 3040, pp. 577–586. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  • Sugihara, G., May, R.M.: Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990)

    Article  Google Scholar 

  • Grigoletto, M.: Bootstrap prediction intervals for autoregressions: Some alternatives. International Journal of Forecasting 14, 447–456 (1998)

    Article  Google Scholar 

  • Lee, Y.-H., Fan, T.-H.: Bootstrapping prediction intervals on stochastic olatility models. Applied Economic Letters 13, 41–45 (2006)

    Article  Google Scholar 

  • Alonso, A.M., Pẽna, D., Romo, J.: Introducing model uncertainty in time series bootstrap. Statistica Sinica 14, 155–174 (2004)

    Google Scholar 

  • Kilian, L.: Accounting for lag uncertainty in autoregressions: The endogenous lag order bootstrap algorithm. Journal of Time Series Analysis 19, 531–548 (1998)

    Article  MATH  Google Scholar 

  • Hurukawa, T., Sakai, S.: Ensemble prediction. Tokyo-doh Press (2004) (in Japanese)

    Google Scholar 

  • Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Chapman and Hall, Boca Raton (1993)

    MATH  Google Scholar 

  • Eckmann, J.P., Kamphorst, S.O., Ruelle, D., Ciliberto, S.: Lyapunov exponents from time series. Physical Review A 34(6), 4971–4979 (1986)

    Article  MathSciNet  Google Scholar 

  • Farmer, J.D., Sidorowich, J.J.: Predicting chaotic time series. Physical Review Letters 59(8), 845–848 (1987)

    Article  MathSciNet  Google Scholar 

  • Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Optics Communications 30(2), 257–261 (1979)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Haraki, D., Suzuki, T., Ikeguchi, T. (2006). Bootstrap Prediction Intervals for Nonlinear Time-Series. In: Corchado, E., Yin, H., Botti, V., Fyfe, C. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2006. IDEAL 2006. Lecture Notes in Computer Science, vol 4224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11875581_19

Download citation

  • DOI: https://doi.org/10.1007/11875581_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45485-4

  • Online ISBN: 978-3-540-45487-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics