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Strong consistency and (weak) distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators of linear and threshold ARCH ( p ) models, with special attention paid to the ARCH (1) and threshold ARCH (1) cases. Conditions supporting these results include (relatively) mild moment existence criteria that enjoy empirical support. These conditions are not shared by competing estimators like OLS. Identification of the TSLS estimators depends on asymmetry, either in the model’s rescaled errors or in the conditional variance function. Monte Carlo studies reveal TSLS estimation can sizably outperform quasi maximum likelihood (QML) in small samples and even best recently proposed two-step estimators specifically designed to enhance the efficiency of QML.

Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE