Advertisement

Statistics and Computing

, Volume 11, Issue 3, pp 229–240 | Cite as

A Conditional Density Approach to the Order Determination of Time Series

  • Bärbel F. Finkenstädt
  • Qiwei Yao
  • Howell Tong
Article

Abstract

The study focuses on the selection of the order of a general time series process via the conditional density of the latter, a characteristic of which is that it remains constant for every order beyond the true one. Using simulated time series from various nonlinear models we illustrate how this feature can be traced from conditional density estimation. We study whether two statistics derived from the likelihood function can serve as univariate statistics to determine the order of the process. It is found that a weighted version of the log likelihood function has desirable robust properties in detecting the order of the process.

conditional density nonparametric regression entropy embedding dimension non-linear stochastic processes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike H. 1972. Information theory and an extension of the maximum likelihood principle. In: Petrov B.N. and Csaki F. (Eds.), Second International Symposium on Information Theory. Akademiai Kiado, Budapest, pp. 267-281.Google Scholar
  2. Auestad B. and Tjøstheim D. 1990. Identification of nonlinear time series: First order characterization and order determination. Biometrika 77: 669-687.Google Scholar
  3. Cheng B. and Tong H. 1992. On consistent nonparametric order determination and chaos (with discussion). Journal of the Royal Statistical Society B 54: 427-474.Google Scholar
  4. Fan J., Yao Q., and Tong H. 1996. Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika. 83: 189-206.Google Scholar
  5. Fan J. and Gijbels I. 1996. Local Polynomial Modelling and its Applications. Chapman and Hall, London.Google Scholar
  6. Hu F., Rosenberger W. and Zidek J.V. 2000. The relevance weighted likelihood for dependent data. Metrika. 51: 223-243.Google Scholar
  7. Kiefer J. 1953. The sequential minimax search for a maximum. Proceedings of the American Mathematical Society. 4: 502-506.Google Scholar
  8. Savit R. and Green M. 1991. Time series and dependent variables. Physica D. 50: 95-116.Google Scholar
  9. Takens F. 1981. Detecting strange attractors in turbulence. In Rand D.A. and Young L.S. (Eds.), Dynamical Systems and Turbulence.Google Scholar
  10. Warwick 1980 Proceedings Lecture Notes in Mathematics 898. Springer, Berlin, pp. 366-381.Google Scholar
  11. Takens F. 1996. Estimation of dimension and order of time series. In: Progress in Nonlinear differential equations and their applications. Birkhäuser, vol. 19, pp. 405-422.Google Scholar
  12. Tong H. 1990. Nonlinear Time Series: A Dynamical System Approach. Oxford: Oxford University Press, Oxford, UK.Google Scholar
  13. Yao Q. and Tong H. 1994. On subset selection in non-parametric stochastic regression. Statistica Sinica. 4: 51-70.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Bärbel F. Finkenstädt
    • 1
  • Qiwei Yao
    • 2
  • Howell Tong
    • 2
    • 3
  1. 1.Department of StatisticsUniversity of WarwickConventryUK
  2. 2.Department of StatisticsLondon School of EconomicsLondonUK
  3. 3.Department of Statistics and Actuarial ScienceThe University of Hong KongPokfulamHong Kong

Personalised recommendations