COMPSTAT pp 307-312 | Cite as

Graphical and phase space models for univariate time series

  • Roland Fried


There are various approaches to model time series data. In the time domain ARMA-models and state space models are frequently used, while phase space models have been applied recently, too. Each approach has got its own strengths and weaknesses w.r.t. parameter estimation, prediction and coping with missing data. We use graphical models to explore and compare the structure of time series models, and focus on interpolation in e.g. seasonal models.


Time series analysis ARMA models phase space embedding conditional independence missing data 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bauer, M., Gather, U. and Imhoff, M. (1998). Analysis of high dimensional data from intensive care medicine. In: R. Payne, P. Green (eds.): Proceedings in Computational Statistics. Heidelberg: Physica Verlag, pp. 185–190.Google Scholar
  2. Bauer, M., Gather, U. and Imhoff, M. (1999). The Identification of Multiple Outliers in Online Monitoring Data. Technical Report 29/1999, Department of Statistics, University of Dortmund, Germany.Google Scholar
  3. Becker, C. and Gather, U. (1999). The Masking Breakdown Point of Multi-variate Outlier Identification Rules. J. Amer. Statist. Assoc., 94, 947–955.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994). Time Series Analysis. Forecasting and Control. Third edition. Englewood Cliffs: Prentice Hall.Google Scholar
  5. Chen, C. and Liu, L.-M. (1993). Joint Estimation of Model Parameters and Outlier Effects in Time Series. J. Americ. Statist. Assoc., 88, 284–297.zbMATHGoogle Scholar
  6. Cox, D.R. and Wermuth, N. (1996). Multivariate Dependencies. London: Chapman and Hall.zbMATHGoogle Scholar
  7. Dawid, A.P. (1979). Conditional Independence in Statistical Theory. J. Roy. Statist. Soc. B, 41, 1–31.MathSciNetzbMATHGoogle Scholar
  8. Delicado, P. and Justel, A. (1999). Forecasting with Missing Data: Application to Coastel Wave Heights. J. Forecasting, 18, 285–298.CrossRefGoogle Scholar
  9. Dempster, A. (1972). Covariance Selection. Biometrics, 28, 157–175.CrossRefGoogle Scholar
  10. Ferreiro, O. (1987). Methodologies for the Estimation of Missing Observations in Time Series. Statistics & Probability Letters, 5, 65–69.MathSciNetzbMATHCrossRefGoogle Scholar
  11. Fried, R. (2000). Exploratory Analysis and a Stochastic Model for Humus-disintegration. Environmental Monitoring and Assessment, (to appear).Google Scholar
  12. Gomez, V., Maravall, A. and Peña, D. (1999). Missing Observations in ARIMA models: Skipping approach versus additive outlier approach. J. Econometrics,88, 341–363.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Harvey, A.C. and Pierse, R.G. (1984). Estimating Missing Observations in Economic Time Series. J. Amer. Statist. Assoc., 79, 125–131.CrossRefGoogle Scholar
  14. Kjaerulff, U. (1995). dHugin: a computational system for dynamic time-sliced Bayesian networks. Int. J. Forecasting, 11, 89–111.CrossRefGoogle Scholar
  15. Lauritzen, S.L. (1996). Graphical Models. Oxford: Clarendon Press.Google Scholar
  16. Lewellen, R.H. and Vessey, S.H. (1999). Analysis of Fragmented Time Series Data Using Box-Jenkins Models. Commun. Statist. - Sim., 28, 667–685.zbMATHCrossRefGoogle Scholar
  17. Packard, N.H., Crutchfield, J.P., Farmer, J.D. and Shaw, R.S. (1980). Geom-etry from a time series. Physical Review Letters, 45, 712–716.CrossRefGoogle Scholar
  18. Smith, J.Q. (1992). A Comparison of the Characteristics of Some Bayesian Forecasting Models. Int. Statist. Rev., 60, 75–87.zbMATHCrossRefGoogle Scholar
  19. Takens, F. (1980). Dynamical Systems and Turbulence. In: Vol. 898 of Lecture Notes in Mathematics. Berlin: Springer-Verlag.Google Scholar
  20. Wermuth, N. and Lauritzen, S.L. (1990). On Substantive Research Hypothe-ses, Conditional Independence Graphs and Graphical Chain Models. J. Roy. Statist. Soc. B, 52, 21–72 (with discussion).MathSciNetzbMATHGoogle Scholar
  21. Wermuth, N. and Scheidt, E. (1977). Fitting a Covariance Selection Model to a Matrix. Applied Statistics, 26, 88–92.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Roland Fried
    • 1
  1. 1.Department of StatisticsUniversity of DortmundDortmundGermany

Personalised recommendations