Skip to main content
SpringerLink
Log in

Graphical and phase space models for univariate time series

  • Conference paper
COMPSTAT

  • 783 Accesses

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • 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 

  • 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 

  • Becker, C. and Gather, U. (1999). The Masking Breakdown Point of Multi-variate Outlier Identification Rules. J. Amer. Statist. Assoc., 94, 947–955.

    Article  MathSciNet  MATH  Google Scholar 

  • 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 

  • 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.

    MATH  Google Scholar 

  • Cox, D.R. and Wermuth, N. (1996). Multivariate Dependencies. London: Chapman and Hall.

    MATH  Google Scholar 

  • Dawid, A.P. (1979). Conditional Independence in Statistical Theory. J. Roy. Statist. Soc. B, 41, 1–31.

    MathSciNet  MATH  Google Scholar 

  • Delicado, P. and Justel, A. (1999). Forecasting with Missing Data: Application to Coastel Wave Heights. J. Forecasting, 18, 285–298.

    Article  Google Scholar 

  • Dempster, A. (1972). Covariance Selection. Biometrics, 28, 157–175.

    Article  Google Scholar 

  • Ferreiro, O. (1987). Methodologies for the Estimation of Missing Observations in Time Series. Statistics & Probability Letters, 5, 65–69.

    Article  MathSciNet  MATH  Google Scholar 

  • Fried, R. (2000). Exploratory Analysis and a Stochastic Model for Humus-disintegration. Environmental Monitoring and Assessment, (to appear).

    Google Scholar 

  • Gomez, V., Maravall, A. and Peña, D. (1999). Missing Observations in ARIMA models: Skipping approach versus additive outlier approach. J. Econometrics,88, 341–363.

    Article  MathSciNet  MATH  Google Scholar 

  • Harvey, A.C. and Pierse, R.G. (1984). Estimating Missing Observations in Economic Time Series. J. Amer. Statist. Assoc., 79, 125–131.

    Article  Google Scholar 

  • Kjaerulff, U. (1995). dHugin: a computational system for dynamic time-sliced Bayesian networks. Int. J. Forecasting, 11, 89–111.

    Article  Google Scholar 

  • Lauritzen, S.L. (1996). Graphical Models. Oxford: Clarendon Press.

    Google Scholar 

  • Lewellen, R.H. and Vessey, S.H. (1999). Analysis of Fragmented Time Series Data Using Box-Jenkins Models. Commun. Statist. - Sim., 28, 667–685.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Smith, J.Q. (1992). A Comparison of the Characteristics of Some Bayesian Forecasting Models. Int. Statist. Rev., 60, 75–87.

    Article  MATH  Google Scholar 

  • Takens, F. (1980). Dynamical Systems and Turbulence. In: Vol. 898 of Lecture Notes in Mathematics. Berlin: Springer-Verlag.

    Google Scholar 

  • 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).

    MathSciNet  MATH  Google Scholar 

  • Wermuth, N. and Scheidt, E. (1977). Fitting a Covariance Selection Model to a Matrix. Applied Statistics, 26, 88–92.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Dortmund, 44221, Dortmund, Germany

    Roland Fried

Authors
  1. Roland Fried
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistical Methods, Statistics Netherlands, P.O. Box 4000, 2270 JM, Voorburg, The Netherlands

    Jelke G. Bethlehem

  2. Faculty of Social Sciences, Department of Methodology and Statistics, Utrecht University, P.O. Box 80140, 3508 TC, Utrecht, The Netherlands

    Peter G. M. van der Heijden

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fried, R. (2000). Graphical and phase space models for univariate time series. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57678-2_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-57678-2_38

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1326-5

  • Online ISBN: 978-3-642-57678-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation