Simple Estimators for the GARCH(1,1) Model

Abstract

I propose closed-form estimators for the GARCH(1,1) model that are based on second-order covariances. The ability to obtain closed-form estimates derives from skewness in the sequence being modeled, which permits separate identification and estimation of the ARCH and GARCH effects. I show these estimators to be CAN under weak stationarity using Martingale limit theory. I also demonstrate conditions under which an iterative GLS estimator reliant on these closed-form estimates as starting values shares the same asymptotic distribution with the QMLE. This asymptotic equivalence is achieved given only third moment existence, which substantially relaxes the moment existence criteria generally required for OLS- and TSLS-style estimators of GARCH processes. The proposed estimators are studied in Monte Carlo experiments and applied to a suite of financial data.

Keywords: GARCH, GMM, closed-form, many moments, skewness

JEL Classification: C13, C22, C53