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.

准最大似然 (QML) 程序在理论上具有吸引力并广泛用于统计推断。虽然有大量关于批处理设置中的 QML 估计的参考资料，但直到最近它才在流设置中引起了很少的关注。研究了一般条件异方差时间序列模型中 QML 过程的收敛特性，并将经典的批量优化例程扩展到流和大规模问题的框架。提出了一个名为 AdaVol 的 GARCH 模型的自适应递归估计程序。AdaVol 过程依赖于随机近似与方差目标估计 (VTE) 技术相结合。这种递归方法具有计算效率高的特性，而 VTE 缓解了通常的 QML 估计由于缺乏凸性而遇到的一些收敛困难。实证结果表明，在 AdaVol 的稳定性和适应现实生活数据的时变估计的能力之间取得了有利的平衡。