Postmodel selection estimators of variance function for nonlinear autoregression

作者：Borkowski Piotr; Mielniczuk Jan^*

来源：Journal of Time Series Analysis, 2010, 31(1): 50-63.

DOI：10.1111/j.1467-9892.2009.00639.x

• Heteroscedastic autoregression
• variance function estimation
• maximum likelihood and pseudolikelihood method
• postmodel selection estimators
• Kullback-Leibler distance
• heavy-tailed data

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.

• 出版日期2010-1