The Quasi-Maximum Likelihood (QML) procedure is widely used for statistical inference due to its robustness against overdisper-sion. However, while there are extensive references on non-recursive QML estimation , recursive QML estimation has attracted little attention until recently. In this paper, we investigate the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model , extending the classical offline optimization routines to recursive approximation. We propose an adaptive recursive estimation routine for GARCH models using the technique of Variance Targeting Estimation (VTE) to alleviate the convergence difficulties encountered in the usual QML estimation . Finally, empirical results demonstrate a favorable trade-off between  the ability to adapt to time-varying estimates and stability of the estimation routine .
 Quasi-Maximum Likelihood (QML) procedures are theoretically appealing and widely used for statistical inference . While there are extensive references on QML estimation in batch settings, the QML estimation in streaming settings has attracted little attention until recently. An investigation of the convergence properties of the QML procedure in a general conditionally heteroscedastic time series model is conducted, and the classical batch optimization routines extended to the framework of streaming and large-scale problems. An adaptive recursive estimation routine for GARCH models named AdaVol is presented. The AdaVol procedure relies on stochastic approximations combined with the technique of Variance Targeting Estimation (VTE) . This recursive method has computationally efficient properties, while VTE alleviates some convergence difficulties encountered by the usual QML estimation due to a lack of convexity. Empirical results demonstrate a favorable trade-off between AdaVol's stability and the ability to adapt to time-varying estimates for real-life data .
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