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, it has attracted little attention in streaming settings 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.

翻译：Qasi-Meximum Lilishood(QML)程序在理论上具有吸引力,并广泛用于统计推论。尽管批量设置中大量提到QML估算,但直到最近,在流流设置中却很少引起注意。在一般的有条件混杂时间序列模型中,对QML程序的趋同特性进行了调查,并将典型的批量优化程序扩大到流流和大规模问题的框架。介绍了名为AdaVol的GRCH模型的适应性循环估算例行程序。AdaVol程序依赖于随机近似,同时采用差异定向估计技术。这一递归方法计算了效率,同时,VTE减轻了通常的QML估计由于缺乏混杂性而遇到的一些趋同困难。经验性结果表明AdaVol的稳定性与适应实时数据时间变化估计的能力之间的有利权衡。