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Construction of Stationary Time Series via the Giggs Sampler with Application to Volatility Models

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  • Pitt, M.K.
  • Walker, S.G.

Abstract

In this paper, we provide a method for modeling stationary time series. We allow the family of marginal densities for the observations to be specified. Our approach is to construct the model with a specified marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. In particular, we present an original application of the Gibbs sampler. We illustrate our approach by fitting a model to time series count data with a marginal Poisson-gamma density.

Suggested Citation

  • Pitt, M.K. & Walker, S.G., 2001. "Construction of Stationary Time Series via the Giggs Sampler with Application to Volatility Models," The Warwick Economics Research Paper Series (TWERPS) 595, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:595
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    File URL: https://warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp595.pdf
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    References listed on IDEAS

    as
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    4. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    5. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
    6. Michael K Pitt & Neil Shephard, "undated". "Filtering via simulation: auxiliary particle filters," Economics Papers 1997-W13, Economics Group, Nuffield College, University of Oxford.
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    More about this item

    Keywords

    VOLATILITY ; TIME SERIES ; EXPECTATIONS;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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