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Time-series Modelling, Stationarity and Bayesian Nonparametric Methods

Author

Listed:
  • Juan Carlos Martínez-Ovando
  • Stephen G. Walker

Abstract

In this paper we introduce two general non-parametric first-order stationary time-series models for which marginal (invariant) and transition distributions are expressed as infinite-dimensional mixtures. That feature makes them the first Bayesian stationary fully non-parametric models developed so far. We draw on the discussion of using stationary models in practice, as a motivation, and advocate the view that flexible (non-parametric) stationary models might be a source for reliable inferences and predictions. It will be noticed that our models adequately fit in the Bayesian inference framework due to a suitable representation theorem. A stationary scale-mixture model is developed as a particular case along with a computational strategy for posterior inference and predictions. The usefulness of that model is illustrated with the analysis of Euro/USD exchange rate log-returns.

Suggested Citation

  • Juan Carlos Martínez-Ovando & Stephen G. Walker, 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
  • Handle: RePEc:bdm:wpaper:2011-08
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    File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7BAAD21931-987D-E2DF-E498-4B23679CD8D4%7D.pdf
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    References listed on IDEAS

    as
    1. Ramsés H. Mena & Stephen G. Walker, 2005. "Stationary Autoregressive Models via a Bayesian Nonparametric Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 789-805, November.
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    3. Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, February.
    4. Michael K. Pitt, 2002. "Constructing First Order Stationary Autoregressive Models via Latent Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 657-663.
    5. Viviane Campos & Chang Dorea, 2005. "Kernel estimation for stationary density of Markov chains with general state space," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 443-453, September.
    6. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    7. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
    8. Pitt, Michael K. & Walker, Stephen G., 2006. "Extended constructions of stationary autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1219-1224, July.
    9. Ramsés Mena & Stephen Walker, 2007. "On the Stationary Version of the Generalized Hyperbolic ARCH Model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 325-348, June.
    10. Barry, Christopher B. & Winkler, Robert L., 1976. "Nonstationarity and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(02), pages 217-235, June.
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    13. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    14. Clements Michael P. & Hendry David F., 2008. "Economic Forecasting in a Changing World," Capitalism and Society, De Gruyter, vol. 3(2), pages 1-20, October.
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    Citations

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    Cited by:

    1. Isadora Antoniano-Villalobos & Stephen G. Walker, 2016. "A Nonparametric Model for Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 126-142, January.

    More about this item

    Keywords

    Stationarity; Markov processes; Dynamic mixture models; Random probability measures; Conditional random probability measures; Latent processes.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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