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A Nonparametric Model for Stationary Time Series

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  • Isadora Antoniano-Villalobos
  • Stephen G. Walker

Abstract

type="main" xml:id="jtsa12146-abs-0001"> Stationary processes are a natural choice as statistical models for time series data, owing to their good estimating properties. In practice, however, alternative models are often proposed that sacrifice stationarity in favour of the greater modelling flexibility required by many real-life applications. We present a family of time-homogeneous Markov processes with nonparametric stationary densities, which retain the desirable statistical properties for inference, while achieving substantial modelling flexibility, matching those achievable with certain non-stationary models. A latent extension of the model enables exact inference through a trans-dimensional Markov chain Monte Carlo method. Numerical illustrations are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:37:y:2016:i:1:p:126-142
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    File URL: http://hdl.handle.net/10.1111/jtsa.12146
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    References listed on IDEAS

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    6. Martínez-Ovando Juan Carlos & Walker Stephen G., 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
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    Cited by:

    1. Matthew Heiner & Athanasios Kottas, 2022. "Autoregressive density modeling with the Gaussian process mixture transition distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 157-177, March.
    2. Jim Griffin & Maria Kalli & Mark Steel, 2018. "Discussion of “Nonparametric Bayesian Inference in Applications”: Bayesian nonparametric methods in econometrics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 207-218, June.
    3. Kalli, Maria & Griffin, Jim E., 2018. "Bayesian nonparametric vector autoregressive models," Journal of Econometrics, Elsevier, vol. 203(2), pages 267-282.
    4. Anzarut, Michelle & Mena, Ramsés H., 2019. "A Harris process to model stochastic volatility," Econometrics and Statistics, Elsevier, vol. 10(C), pages 151-169.

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