×

zbMATH — the first resource for mathematics

Nonlinear time series analysis since 1990: Some personal reflections. (English) Zbl 1018.37049
The author reflects upon the developments of the nonlinear time series analysis since 1990 focusing on the following five directions which he believes are the most promising: the interface between the nonlinear time series analysis and chaos, the nonparametric and semiparametric approach, nonlinear state space modeling, nonlinear modeling of panels of time series, and financial series in both discrete and continuous time. The author finishes the paper by predicting even faster and exciting developments of the subject in the next twenty years.

MSC:
37M10 Time series analysis of dynamical systems
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B84 Economic time series analysis
37-03 History of dynamical systems and ergodic theory
01A05 General histories, source books
Software:
FinTS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] An, H.: A note on chaotic maps and time series. In: Athens Conference on Applied Probability and Time Series, Vol.2, 15–26, 1996
[2] An, H., Cheng, B.: A Kolmogorov-Smirnov type statistic with application to test for nonlinearity in time series. Int. Statist. Rev., 59: 287–307 (1991) · Zbl 0748.62049
[3] Chan, K.S., Tong, H.: Chaos: a statistical perspective. Springer-Verlag, New York, 2001 · Zbl 0977.62002
[4] Chan, K.S., Tong, H.: A note on the equivalence of two approaches for specifying a markov process. Bernoulli, (2002) (to appear) · Zbl 1002.60071
[5] Chan, W.S., Li, W.K., Tong, H.: Proceedings of the Hong Kong international workshop on statistics and finance: an interface. Imperial College Press, London, 2000
[6] Cox, D.R.: The current position of statistics: a personal view. Int. Stat. Rev., 65: 261–276 (1997) · Zbl 0932.62002
[7] Durbin, J., Koopman, S.J.: Time series analysis by state space methods. Oxford University Press, Oxford, 2001 · Zbl 0995.62504
[8] Fan, J., Gijbels, I.: Local polynomial modelling and its applications. Chapman and Hall, London, 1996 · Zbl 0873.62037
[9] Fan, J., Yao, Q.: Nonlinear time series: nonparametric and parametric methods. Springer-Verlag, New York, 2002 · Zbl 1014.62103
[10] Fitzgerald, W.J., Smith, R.L., Walden, A.T., Young, P.C.: Nonlinear and nonstationary signal processing. Cambridge Univ. Press, Cambridge, 2000 · Zbl 0958.00020
[11] Friedman, J.H., Steutzle, W.: Projection pursuit regression. J. Am. Statist. Ass., 76: 817–823 (1981)
[12] Gelfand, A.E., Smith, A.F.M. Sampling based approaches to calculating marginal densities. J. Amer. Stat. Ass., 85: 398–409 (1990) · Zbl 0702.62020
[13] Kitagawa, G.: Non-Gaussian state space modelling of non-stationary time series. J. Am. Stat. Assoc., 82: 1032–1063 (1987) · Zbl 0644.62088
[14] Kitagawa, G., Gersch, W.: Smoothness priors analysis and time series. Springer Verlag, New York, 1996 · Zbl 0853.62069
[15] Li, M-C., Chan, K.S.: Semiparametric reduced-rank regression. Tech. Rep., Department of Statistics, Univ. Iowa, U.S.A., 2001
[16] Poincaré, H.: Science et méthode. Paris: Earnest Flammarion. (English Translation: Science and Method, New York, Dover, 1952), 1908
[17] Robinson, P.M.: Non-parametric estimation for time series models. J. Time Series Anal., 4: 185–208 (1983) · Zbl 0544.62082
[18] Stenseth, N.C., Chan, K.S., Tong, H., Boonstra, R., Boutin, S., Krebs, C.J., Post, E., O’Donoghue, M., Yoccoz, N.G., Forchhammer, M.C., Hurrell, J.W.: Common dynamic structure of canadian lynx populations within three climatic regions. Science, 285: 1071–1073 (1999)
[19] Tjøstheim, D. Non-linear time series: a selective review. Scan. J. Statist., 21: 97–130 (1994) · Zbl 0799.62098
[20] Tong, H.: Non-linear time series: a dynamical system approach. Oxford University Press, Oxford, 1990 · Zbl 0716.62085
[21] Tsay, R.: Analysis of financial time series. J. Wiley, New York, 2002 · Zbl 1037.91080
[22] Xia, Y., Tong, H., Li, W.K., Zhu, L.: An adaptive estimation of dimension reduction space. J. Roy. Statist. Soc. (Series B), (to appear) · Zbl 1091.62028
[23] Yao, Q., Tong, H., Finkenstädt, B., Stenseth, N.C.: Common structure in panels of short ecological timeseries. Proc. R. Soc. Lond. (Series B), 267: 1–9 (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.