Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Discussion Paper Series 1 ; No. 2002,26

Classification and Topics

• Classification: Wirtschaft ; Model Evaluation, Validation, and Selection ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Statistical Simulation Methods: General
• Subject: wild bootstrap ; pairwise bootstrap ; robust inference ; Bootstrap-Verfahren ; ARCH-Modell ; Stochastischer Prozess ; Volatilität ; Zeitreihenanalyse ; Heteroskedastizität ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Kilian, Lutz ; Gonçalves, Sílvia
• Event: Veröffentlichung
• (who): Deutsche Bundesbank
• (where): Frankfurt a. M.
• (when): 2002

Further information

• Handle: http://hdl.handle.net/10419/19583
• Last update: 10.03.2025, 11:45 AM CET