zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
37M10Time series analysis (dynamical systems)
62M10Time series, auto-correlation, regression, etc. (statistics)
91B84Economic time series analysis
37-03Historical (Dynamical systems and ergodic theory)
01A05General histories, source books
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 · doi:10.2307/1403689
[3]Chan, K.S., Tong, H.: Chaos: a statistical perspective. Springer-Verlag, New York, 2001
[4]Chan, K.S., Tong, H.: A note on the equivalence of two approaches for specifying a markov process. Bernoulli, (2002) (to appear)
[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) · doi:10.1111/j.1751-5823.1997.tb00305.x
[7]Durbin, J., Koopman, S.J.: Time series analysis by state space methods. Oxford University Press, Oxford, 2001
[8]Fan, J., Gijbels, I.: Local polynomial modelling and its applications. Chapman and Hall, London, 1996
[9]Fan, J., Yao, Q.: Nonlinear time series: nonparametric and parametric methods. Springer-Verlag, New York, 2002
[10]Fitzgerald, W.J., Smith, R.L., Walden, A.T., Young, P.C.: Nonlinear and nonstationary signal processing. Cambridge Univ. Press, Cambridge, 2000
[11]Friedman, J.H., Steutzle, W.: Projection pursuit regression. J. Am. Statist. Ass., 76: 817–823 (1981) · doi:10.2307/2287576
[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 · doi:10.2307/2289776
[13]Kitagawa, G.: Non-Gaussian state space modelling of non-stationary time series. J. Am. Stat. Assoc., 82: 1032–1063 (1987) · Zbl 0644.62088 · doi:10.2307/2289375
[14]Kitagawa, G., Gersch, W.: Smoothness priors analysis and time series. Springer Verlag, New York, 1996
[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 · doi:10.1111/j.1467-9892.1983.tb00368.x
[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) · doi:10.1126/science.285.5430.1071
[19]Tjøstheim, D. Non-linear time series: a selective review. Scan. J. Statist., 21: 97–130 (1994)
[20]Tong, H.: Non-linear time series: a dynamical system approach. Oxford University Press, Oxford, 1990
[21]Tsay, R.: Analysis of financial time series. J. Wiley, New York, 2002
[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)
[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) · doi:10.1098/rspb.2000.1306