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.
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Lorenz, E.N.: Atmospheric predictability as revealed by naturally occurring analogues. J. Atmospheric Sciences 26, 636–646 (1969)
Sano, M., Sawada, Y.: Measurement of the lyapunov spectrum from a chaotic time series. Physical Review Letters 55(10), 1082–1085 (1985)
Haraki, D., Suzuki, T., Ikeguchi, T.: Bootstrap Nonlinear Prediction. submitted to Physical Review E (2005)
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)
Sugihara, G., May, R.M.: Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 344, 734–741 (1990)
Grigoletto, M.: Bootstrap prediction intervals for autoregressions: Some alternatives. International Journal of Forecasting 14, 447–456 (1998)
Lee, Y.-H., Fan, T.-H.: Bootstrapping prediction intervals on stochastic olatility models. Applied Economic Letters 13, 41–45 (2006)
Alonso, A.M., Pẽna, D., Romo, J.: Introducing model uncertainty in time series bootstrap. Statistica Sinica 14, 155–174 (2004)
Kilian, L.: Accounting for lag uncertainty in autoregressions: The endogenous lag order bootstrap algorithm. Journal of Time Series Analysis 19, 531–548 (1998)
Hurukawa, T., Sakai, S.: Ensemble prediction. Tokyo-doh Press (2004) (in Japanese)
Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Chapman and Hall, Boca Raton (1993)
Eckmann, J.P., Kamphorst, S.O., Ruelle, D., Ciliberto, S.: Lyapunov exponents from time series. Physical Review A 34(6), 4971–4979 (1986)
Farmer, J.D., Sidorowich, J.J.: Predicting chaotic time series. Physical Review Letters 59(8), 845–848 (1987)
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)
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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
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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
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