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Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

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Author Info
Sílvia Gonçalves ()
Lutz Kilian

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Abstract

Conditional heteroskedasticity is an important feature of many macroeconomic and financial time series. Standard residual-based bootstrap procedures for dynamic regression models treat the regression error as i.i.d. These procedures are invalid in the presence of conditional heteroskedasticity. We establish the asymptotic validity of three easy-to-implement alternative bootstrap proposals for stationary autoregressive processes with m.d.s. errors subject to possible conditional heteroskedasticity of unknown form. These proposals are the fixed-design wild bootstrap, the recursive-design wild bootstrap and the pairwise bootstrap. In a simulation study all three procedures tend to be more accurate in small samples than the conventional large-sample approximation based on robust standard errors. In contrast, standard residual-based bootstrap methods for models with i.i.d. errors may be very inaccurate if the i.i.d. assumption is violated. We conclude that in many empirical applications the proposed robust bootstrap procedures should routinely replace conventional bootstrap procedures for autoregressions based on the i.i.d. error assumption.

La présence d'hétéroscédasticité conditionnelle est une caractéristique importante de beaucoup de séries temporelles en macroéconomie et en finance. Les méthodes de bootstrap usuelles pour des modèles de régression dynamiques rééchantillonnent les erreurs de façon i.i.d. et ne sont pas valables sous la présence d'hétéroscédasticité conditionnelle. Dans ce papier, nous montrons la validité asymptotique de trois méthodes de bootstrap pour des processus stationnaires autorégressifs dont le terme d'erreur est une différence de martingale. Les méthodes de bootstrap que nous étudions sont le "wild" bootstrap fixé, le "wild" bootstrap récursif et le bootstrap par couples. Une étude de Monte Carlo montre que la performance d'intervalles de confiance basées sur ces méthodes est supérieure à celle des intervalles de confiance basées sur la théorie asymptotique robuste à la présence d'hétéroscédasticité. Par contre, la performance de la méthode de bootstrap usuelle basée sur l'hypothèse i.i.d. des erreurs peut être très mauvaise si les erreurs sont hétéroscédastiques. Nous concluons que les méthodes de bootstrap robustes étudiées dans ce papier doivent remplacer la méthode de bootstrap usuelle dans des applications de bootstrap pour des modèles autorégressifs stationnaires.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-17.

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Date of creation: 01 Apr 2003
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Handle: RePEc:cir:cirwor:2003s-17

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Keywords: Conditional Heteroskedasticity; Wild Bootstrap; Pairwise Bootstrap; hétéroscédasticité conditionnelle; wild bootstrap; bootstrap par couples;

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