Simple Estimators for GARCH Models

32 Pages Posted: 13 Jan 2017 Last revised: 27 Jan 2017

Date Written: January 11, 2017


Closed-form estimators are developed for the popular GARCH(1,1) and threshold GARCH(1,1) models, with select results extending to the general GARCH(p, q) model. Identification sources to asymmetry, either in the distribution of rescaled errors or in the conditional variance function. Given empirically-relevant moment existence criteria, properties of regular variation coupled with point process theory establish the distributional limits of these estimators to be stable though highly non-normal, with slow convergence rates. Monte Carlo experiments evidence superior finite sample performance of the closed-form estimators over the VTE and QMLE in (relatively) small samples when the model's rescaled errors are heavily skewed. In these cases, the closed-form estimators also offer a means for enhancing the (finite sample) efficiency of both the VT and QML estimates in a two-stage estimation procedure.

Supplemental appendix can be found at:

Keywords: GARCH Models, Closed Form Estimation, Heavy Tails, Instrumental Variables, Regular Variation

JEL Classification: C13, C22, C58

Suggested Citation

Prono, Todd, Simple Estimators for GARCH Models (January 11, 2017). Available at SSRN: or

Todd Prono (Contact Author)

Federal Reserve Board ( email )

20th and Constitution Ave NW
Washington, DC 20551
United States

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