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Time-series Modelling, Stationarity and Bayesian Nonparametric Methods

Author

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  • Martínez-Ovando Juan Carlos
  • Walker Stephen G.

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

  • Martínez-Ovando Juan Carlos & Walker Stephen G., 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: https://www.banxico.org.mx/publications-and-press/banco-de-mexico-working-papers/%7BC01450C9-01C9-B4BF-03B4-4C6ADC9190F0%7D.pdf
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    References listed on IDEAS

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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.

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    More about this item

    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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