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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 ...
Regular Variation of Popular GARCH Processes Allowing for Distributional Asymmetry
Linear GARCH(1,1) and threshold GARCH(1,1) processes are established as regularly varying, meaning their heavy tails are Pareto like, under conditions that allow the innovations from the, respective, processes to be skewed. Skewness is considered a stylized fact for many financial returns assumed to follow GARCH-type processes. The result in this note aids in establishing the asymptotic properties of certain GARCH estimators proposed in the literature.
When Simplicity Offers a Benefit, Not a Cost: Closed-Form Estimation of the GARCH(1,1) Model that Enhances the Efficiency of Quasi-Maximum Likelihood
Simple, multi-step estimators are developed for the popular GARCH(1,1) model, where these estimators are either available entirely in closed form or dependent upon a preliminary estimate from, for example, quasi-maximum likelihood. Identification sources to asymmetry in the model's innovations, casting skewness as an instrument in a linear, two-stage least squares estimator. Properties of regular variation coupled with point process theory establish the distributional limits of these estimators as stable, though highly non-Gaussian, with slow convergence rates relative to the ??n-case. Moment ...