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Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

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Author Info
Kilian, Lutz
Gonçalves, Sílvia

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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-toimplement 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 based on the i.i.d. error assumption.

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Paper provided by Deutsche Bundesbank, Research Centre in its series Discussion Paper Series 1: Economic Studies with number 2002,26.

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Date of creation: 2002
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Handle: RePEc:zbw:bubdp1:4191

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Related research
Keywords: wild bootstrap; pairwise bootstrap; robust inference;

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Find related papers by JEL classification:
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods

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