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.

翻译：Qasi-Meximum Liblihood(QML)程序在理论上具有吸引力,并广泛用于统计推断。尽管批量设置中大量提到QML估计,但流流环境中的QML估计直到最近才引起注意。调查了一般有条件混凝土时间序列模型中QML程序趋同特性,并将典型的批量优化程序扩大到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计程序。AdaVol程序依赖于随机近似,加上差异定向估计技术。这一循环方法具有计算效率,而VTE则减轻了通常的QML估计由于缺乏凝固性而遇到的一些趋同困难。经验性结果显示AdaVol的稳定性与适应实时数据时间变化估计的能力之间有着有利的权衡。