Variance Targeting for Heavy Tailed Time Series

The estimation of GARCH models by QML with variance targeting requires at least a ...nite unconditional fourth moment in the observed data  to ensure Gaussian asymptotics. However, many ...nancial returns series may not have a fourth moment. We robustify the method against heavy tails by exploiting new tail-trimming techniques for both the ...rst step variance estimator and the second step criterion. We propose two estimators, the ...rst of which is based on the QML loss when the error [ ]  1 yet [ 4  ] = 1 is allowed. The second imbeds QML estimating equations with over identifying conditions into GMM criteria allowing for [ ] = 1. Both estimators are consistent and asymptotically normal, where di¤erent rates of convergence and asymptotic scales arise if [  ] = 1 and [ 4  ]  1, or [ 4  ] = 1. A Monte Carlo study reveals the merits of the new estimators.