Bootstrapping autoregressions with conditional heteroskedasticity of unknown form

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 e...

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Bibliographic Details
Published in:Journal of econometrics Vol. 123; no. 1; pp. 89 - 120
Main Authors: Gonçalves, Sı́lvia, Kilian, Lutz
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.11.2004
Elsevier
Elsevier Sequoia S.A
Series:Journal of Econometrics
Subjects:
Applications
Autoregressions
Bootstrap
Bootstrap mechanism
Bootstrap method
Bootstrapping
Conditional heteroskedasticity
Econometrics
Economic models
Economic theory
Errors
Exact sciences and technology
Inference from stochastic processes; time series analysis
Insurance, economics, finance
Linear inference, regression
Macroeconomics
Mathematical models
Mathematics
Nonparametric inference
Probability and statistics
Recursion
Regression analysis
Sciences and techniques of general use
Simulation
Statistics
Studies
Time series
Wild bootstrap
Wild bootstrap
Conditional heteroskedasticity
Bootstrap
C22
Autoregressions
C15
Data analysis
Autoregression
Conditional distribution
Error estimation
Martingale
Time series
Statistical estimation
Statistical simulation
Economic data
Statistical method
Regression model
Experimental design
Approximation error
Stationary process
Econometrics
Dynamic model
Autoregressive processes
ISSN:0304-4076, 1872-6895
Online Access:Get full text
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Summary: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 martingale difference 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.
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ISSN:0304-4076
1872-6895
DOI:10.1016/j.jeconom.2003.10.030