Abstract
In this paper we propose a bootstrap method for quasi-maximum likelihood (QML) estimators in GARCH(1,1) models. The wild bootstrap is used to bootstrap GARCH(1,1) processes and construct bootstrap QML estimators. It is shown that this bootstrap procedure “works” in the sense that it is consistent. Simulation results demonstrate the small sample behaviour of the proposed bootstrap method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bollerslev T. Generalized autoregressive conditional heteroskedasticity, J. Econometrics 1986, 31:307–327.
Drost F. C., Klaassen C. A. J. Efficient estimation in semiparametric GARCH models, Preprint, 1996, to appear in J. Econometrics.
Efron B. Bootstrap methods: Another look at the jackknife, Ann. Statist. 1979, 7:1–26.
Engle R. F. Autoregressive conditional heteroscedasticity with estimates of the variance of U.K. inflation, Econometrica 1982, 50:987–1007.
Engle R. F. (ed.) ARCH: Selected Readings, Oxford University Press, Oxford, 1995.
Engle R. F., Bollerslev T. Modelling the persistence of conditional variances, Econometric Reviews 1986, 5:1–50, 81-87.
Engle R. F., Gonzáles-Rivera G. Semiparametric ARCH models, J. Business and Economic Statist. 1991,9:345–359.
Franke J., Kreiss J.-R, Mammen E. Bootstrap for kernel smoothing in nonlinear time series, Preprint 97/03, Technical University Braunschweig, 1997, submitted to Bernoulli.
Härdle W., Mammen E. Comparing nonparametric versus parametric regression fits, Ann. Statist. 1993, 21:1926–1947.
Lee S.-W., Hansen B. E. Asymptotic theory for the GARCH(1,1) quasi-maximum likelihood estimator, Econometric Theory 1994, 10:29–52.
Maercker G. Statistical Inference in Conditional Heteroskedastic Autoregressive Models, Shaker, Aachen, 1997.
Mammen E. When Does Bootstrap Work? Lecture Notes in Statistics 77, Springer, New York, 1992.
Neumann M. H., Kreiss J.-P. Regression-type inference in nonparametric autoregression, Preprint, 1998, submitted to Ann. Statist.
Weiss A. A. Asymptotic theory for ARCH models: estimation and testing, Econometric Theory 1986, 2:107–131.
Wu C. F. J. Jackknife, bootstrap and other resampling methods in regression analysis, Ann. Statist. 1986, 14:1261–1343.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Maercker, G. (1998). Bootstrapping Garch(1,1) Models. In: Refenes, AP.N., Burgess, A.N., Moody, J.E. (eds) Decision Technologies for Computational Finance. Advances in Computational Management Science, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5625-1_16
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5625-1_16
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-8309-3
Online ISBN: 978-1-4615-5625-1
eBook Packages: Springer Book Archive