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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.

Suggested Citation

  • Sílvia Gonçalves & Lutz Kilian, 2003. "Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity," CIRANO Working Papers 2003s-28, CIRANO.
  • Handle: RePEc:cir:cirwor:2003s-28

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    Cited by:

    1. Xu, Ke-Li & Phillips, Peter C.B., 2008. "Adaptive estimation of autoregressive models with time-varying variances," Journal of Econometrics, Elsevier, vol. 142(1), pages 265-280, January.
    2. Tommaso Proietti & Alessandro Giovannelli, 1705. "A Durbin-Levinson Regularized Estimator of High Dimensional Autocovariance Matrices," CREATES Research Papers 2017-20, Department of Economics and Business Economics, Aarhus University.
    3. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2009. "Co-integration rank tests under conditional heteroskedasticity," Discussion Papers 09/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    4. Serguei Zernov & Victoria Zindle-Walsh & John Galbraith, 2006. "Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions," Departmental Working Papers 2006-16, McGill University, Department of Economics.
    5. International Monetary Fund, 2009. "Uganda and Rwanda; Selected Issues," IMF Staff Country Reports 09/36, International Monetary Fund.

    More about this item


    infinite autoregression; conditional heteroskedasticity; wild bootstrap; pairwise bootstrap; autoregression d'ordre infini; hétéroscédasticité conditionnelle; wild bootstrap; bootstrap par couples;

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