Estimating the Lyapunov exponent from chaotic time series with dynamic noise

Statistical Methodology

Volumn 4, Issue 4, 2007, Pages 461-480

  Yonemoto, Koji ^a   Yanagawa, Takashi ^b  

^a KYUSHU UNIVERSITY   (Japan)

^b KURUME UNIVERSITY   (Japan)

Author keywords

symbol mixing; Delay time; Embedding dimension; Lyapunov exponent; Nadaraya Watson kernel type estimator

Indexed keywords

EID: 34548482976     PISSN: 15723127     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.stamet.2007.02.001     Document Type: Article

References (18)

1. An H.Z., and Huang F.C. The geometric ergodicity of nonlinear autoregressive models. Stat. Sinica 6 (1996) 943-956
2. Bradley R. Basic properties of strong mixing conditions. In: Eberlein E., and Taqqu M.S. (Eds). Dependence in Probability and Statistics: A Survey of Recent Results (1986), Birkhäuser, Boston 165-192
3. Cawley R., and Hsu G. Local-geometric-projection method for noise reduction in chaotic maps and flows. Phys. Rev. A 46 (1992) 3057-3082
4. Chan K.S., and Tong H. A note on noisy chaos. J. R. Stat. Soc. Ser. B 56 2 (1994) 301-311
5. Collomb G. Propriétés de convergence presque complète du prédicteur à noyau. Z. Wahrscheinlichkeitstheorie verw. Geviete 66 (1984) 441-460
6. Dennis B., Desharnais R.A., Cushing J.M., Henson S.M., and Costantino R.F. Can noise induce chaos?. OIKOS 102 (2003) 329-339
7. Fueda K., and Yanagawa T. Estimating the embedding dimension and delay time from chaotic time series with dynamic noise. J. Japan Statist. Soc. 31 1 (2001) 27-38
8. Henon M. A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50 (1976) 69-77
9. Kostelich K., and Yorke J.A. Noise reduction-finding the simplest dynamical system consistent with the data. Physica D 41 (1990) 183-196
10. Landa P.S., and Rozenblum M.G. A comparison of methods for constructing a phase space and determining the dimension of an attractor from experimental data. Sov. Phys. Tech. Phys. 34 (1989) 1229-1232
11. McCaffrey D.F., Ellner S., Gallant A.R., and Nychka D. Estimating the Lyapunov exponent of a chaotic system with nonparametric regression. J. Amer. Statist. Assoc. 87 (1992) 682-695
12. Nadaraya E.A. On estimating regression. Theory Probab. Appl. 9 (1964) 141-142
13. Pikovsky A.S. Discrete-time dynamic noise filtering. Radio. Eng. Electron. Phys. 9 (1986) 81
14. Sauer T. A noise reduction method for signals from nonlinear systems. Physica D 58 (1992) 193-201
15. Watson G.S. Smooth regression analysis. Sankhyā Ser. A 26 (1964) 359-372
16. Whang Y., and Linton O. The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series. J. Econometrics 91 (1999) 1-42
17. Yao Q., and Tong H. Quantifying the influence of initial value on nonlinear prediction. J. R. Stat. Soc. B56 (1994) 701-725
18. Yonemoto K., and Yanagawa T. Estimating the embedding dimension and delay time of chaotic time series by an autoregressive model. Bull. Inform. Cybernet. 33 1-2 (2001) 53-62