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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Vydáno v:	Journal of econometrics Ročník 123; číslo 1; s. 89 - 120
Hlavní autoři:	Gonçalves, Sı́lvia, Kilian, Lutz
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.11.2004 Elsevier Elsevier Sequoia S.A
Edice:	Journal of Econometrics
Témata:	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
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Shrnutí:	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.
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0304-4076 1872-6895
DOI:	10.1016/j.jeconom.2003.10.030