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Working Paper
When Tails Are Heavy: The Benefits of Variance-Targeted, Non-Gaussian, Quasi-Maximum Likelihood Estimation of GARCH Models
In heavy-tailed cases, variance targeting the Student's-t estimator proposed in Bollerslev (1987) for the linear GARCH model is shown to be robust to density misspecification, just like the popular Quasi-Maximum Likelihood Estimator (QMLE). The resulting Variance-Targeted, Non-Gaussian, Quasi-Maximum Likelihood Estimator (VTNGQMLE) is shown to possess a stable limit, albeit one that is highly non-Gaussian, with an ill-defined variance. The rate of convergence to this non-standard limit is slow relative √n and dependent upon unknown parameters. Fortunately, the sub-sample bootstrap is ...
Working Paper
Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance
Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported empirically by many (high frequency) financial returns. These conditions are not shared by competing closed-form estimators like OLS. Identification of these TSLS estimators depends on asymmetry, either in the model's rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS ...