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Filtering With Heavy Tails

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  • Andrew Harvey
  • Alessandra Luati

Abstract

An unobserved components model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation-driven model, based on a conditional Student's t -distribution, which is tractable and retains some of the desirable features of the linear Gaussian model. Letting the dynamics be driven by the score of the conditional distribution leads to a specification that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The methods are illustrated with an application to rail travel in the United Kingdom. The final part of the article shows how the model may be extended to include explanatory variables.

Suggested Citation

  • Andrew Harvey & Alessandra Luati, 2014. "Filtering With Heavy Tails," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1112-1122, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1112-1122
    DOI: 10.1080/01621459.2014.887011
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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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