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Postmodel selection estimators of variance function for nonlinear autoregression

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  • Piotr Borkowski
  • Jan Mielniczuk

Abstract

We consider a problem of estimating a conditional variance function of an autoregressive process. A finite collection of parametric models for conditional density is studied when both regression and variance are modelled by parametric functions. The proposed estimators are defined as the maximum likelihood estimators in the models chosen by penalized selection criteria. Consistency properties of the resulting estimator of the variance when the conditional density belongs to one of the parametric models are studied as well as its behaviour under mis‐specification. The autoregressive process does not need to be stationary but only existence of a stationary distribution and ergodicity is required. Analogous results for the pseudolikelihood method are also discussed. A simulation study shows promising behaviour of the proposed estimator in the case of heavy‐tailed errors in comparison with local linear smoothers.

Suggested Citation

  • Piotr Borkowski & Jan Mielniczuk, 2010. "Postmodel selection estimators of variance function for nonlinear autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 50-63, January.
    • Handle: RePEc:bla:jtsera:v:31:y:2010:i:1:p:50-63
    DOI: 10.1111/j.1467-9892.2009.00639.x
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    References listed on IDEAS

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