Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form
University of Montreal - Department of Economics
University of Michigan at Ann Arbor - Department of Economics; Centre for Economic Policy Research (CEPR)
ECB Working Paper No. 196
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 based on the i.i.d. error assumption.
Number of Pages in PDF File: 49
Keywords: Wild bootstrap, pairwise bootstrap, robust inference, GARCH, stochastic volatility
JEL Classification: C15, C22, C52working papers series
Date posted: April 9, 2003
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