时间序列可预测漂移参数的在线跟踪
Online Tracking of a Predictable Drifting Parameter of a Time Series
摘要：
我们提出了一个在线算法来跟踪一个多维时变参数的时间序列，这也被允许是一个可预测的过程相对于底层的时间序列。该算法由增益函数驱动。在增益的假设下，我们推导出一致的非渐近误差界的跟踪算法中选择的步长的算法和感兴趣的参数的变化。我们还概述了如何适当的增益函数可以构建。我们给出了几个例子，不同的变分设置的参数过程中，我们的结果可以应用。所提出的方法涵盖了许多框架和模型（包括经典的Robbins-Monro和Kiefer-Wolfowitz程序），其中随机逼近算法包括数据分析的主要推理工具。我们在一些细节处理一对夫妇的具体模型。
英文摘要：
We propose an online algorithm for tracking a multidimensional time-varying parameter of a time series, which is also allowed to be a predictable process with respect to the underlying time series. The algorithm is driven by a gain function. Under assumptions on the gain, we derive uniform non-asymptotic error bounds on the tracking algorithm in terms of chosen step size for the algorithm and the variation of the parameter of interest. We also outline how appropriate gain functions can be constructed. We give several examples of different variational setups for the parameter process where our result can be applied. The proposed approach covers many frameworks and models (including the classical Robbins-Monro and Kiefer-Wolfowitz procedures) where stochastic approximation algorithms comprise the main inference tool for the data analysis. We treat in some detail a couple of specific models.
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