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Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity

  • Sílvia Gonçalves
  • Lutz Kilian

The main contribution of this paper is twofold. First, we derive the consistency and asymptotic normality of the estimated autoregressive sieve parameters when the data are generated by a stationary linear process with martingale difference errors that are possibly subject to conditional heteroskedasticity of unknown form. To the best of our knowledge, the asymptotic distribution of the least-squares estimator has not been derived under these conditions. Second, we show that a suitably constructed bootstrap estimator will have the same limit distribution as the OLS estimator. Our results provide theoretical justification for the use of either the conventional asymptotic approximation or the bootstrap approximation of the distribution of smooth functions of autoregressive parameters. La contribution de ce papier est double. Premièrement, nous dérivons les propriétés asymptotiques (convergence et normalité asymptotique) des estimateurs de moindre carrés ordinaires des paramètres autoregressifs dans le cadre de modèles autoregressifs d'ordre infini dont les innovations sont des différences de martingale possiblement hétéroscédastiques. Deuxièmement, nous démontrons la validité asymptotique d'une méthode de bootstrap dans ce contexte. Nos résultats justifient théoriquement l'utilisation de la loi asymptotique ou l'utilisation de la distribution de bootstrap comme méthodes d'inférence pour les paramètres autoregressifs ou les fonctions de ceux-ci.

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File URL: http://www.cirano.qc.ca/files/publications/2003s-28.pdf
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Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-28.

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Length: 35 pages
Date of creation: 01 May 2003
Date of revision:
Handle: RePEc:cir:cirwor:2003s-28
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