Advertisement

Time Series

  • Jean-Michel Marin
  • Christian P. Robert
Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

At one point or another, everyone has to face modeling time series datasets, by which we mean series of dependent observations that are indexed by time (like both series in the picture above!). As in the previous chapters, the difficulty in modeling such datasets is to balance the complexity of the representation of the dependence structure against the estimation of the corresponding model—and thus the modeling most often involves model choice or model comparison. We cover here the Bayesian processing of some of the most standard time series models, namely the autoregressive and moving average models, as well as extensions that are more complex to handle like stochastic volatility models used in finance.

Keywords

Hide Markov Model Posterior Distribution Move Average Gibbs Sampler Hide State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Brockwell, P. and Davis, P. (1996). Introduction to Time Series and Forecasting. Springer Texts in Statistics. Springer-Verlag, New York.CrossRefMATHGoogle Scholar
  2. Cappé, O., Moulines, E., and Rydén, T. (2004). Hidden Markov Models. Springer-Verlag, New York.Google Scholar
  3. Chib, S. (1995). Marginal likelihood from the Gibbs output. J. American Statist. Assoc., 90:1313–1321.MathSciNetCrossRefMATHGoogle Scholar
  4. Del Moral, P., Doucet, A., and Jasra, A. (2006). Sequential Monte Carlo samplers. J. Royal Statist. Soc. Series B, 68(3):411–436.CrossRefMATHGoogle Scholar
  5. Frühwirth-Schnatter, S. (2006). Finite Mixture and Markov Switching Models. Springer-Verlag, New York, New York.MATHGoogle Scholar
  6. Gouriéroux, C. (1996). ARCH Models. Springer-Verlag, New York.Google Scholar
  7. Green, P. (1995). Reversible jump MCMC computation and Bayesian model determination. Biometrika, 82(4):711–732.MathSciNetCrossRefMATHGoogle Scholar
  8. Marin, J.-M. and Robert, C. (2007). Bayesian Core. Springer-Verlag, New York.MATHGoogle Scholar
  9. McDonald, I. and Zucchini, W. (1997). Hidden Markov and other models for discrete-valued time series. Chapman and Hall/CRC, London.Google Scholar
  10. Robert, C. (2007). The Bayesian Choice. Springer-Verlag, New York, paperback edition.Google Scholar
  11. Robert, C. and Casella, G. (2004). Monte Carlo Statistical Methods. Springer-Verlag, New York, second edition.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Jean-Michel Marin
    • 1
  • Christian P. Robert
    • 2
  1. 1.Université Montpellier 2MontpellierFrance
  2. 2.Université Paris-DauphineParisFrance

Personalised recommendations