Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

49 Pages Posted: 9 Apr 2003

See all articles by Sílvia Gonçalves

Sílvia Gonçalves

University of Montreal - Department of Economics

Lutz Kilian

University of Michigan at Ann Arbor - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: November 2002

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

Keywords: Wild bootstrap, pairwise bootstrap, robust inference, GARCH, stochastic volatility

JEL Classification: C15, C22, C52

Suggested Citation

Goncalves, Silvia and Kilian, Lutz, Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form (November 2002). ECB Working Paper No. 196. Available at SSRN: https://ssrn.com/abstract=358520

Silvia Goncalves

University of Montreal - Department of Economics ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7
Canada

Lutz Kilian (Contact Author)

University of Michigan at Ann Arbor - Department of Economics ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States
734-764-2320 (Phone)
734-764-2769 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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