标题： 在线估计方法用于不规则自回归模型 显示英文标题

标题： Online estimation methods for irregular autoregressive models

摘要： 在过去的几十年里，由于观察到的巨大技术增长，时间数据的集合迅速积累大量数据变得越来越常见。 这为通过估计越来越精确的模型来提取有价值的信息提供了机会。 但同时，它也带来了持续更新模型的挑战，因为新的数据不断出现。 目前可用的方法来解决这个问题，即所谓的在线学习方法，使用当前的参数估计和新数据来更新估计器。 这些方法避免使用完整的原始数据并加快计算速度。 在本工作中，我们考虑了三种在线学习算法，用于时间序列模型中的参数估计。 特别是，实现的方法是：梯度下降、牛顿步和卡尔曼滤波递归。 这些算法应用于最近开发的不规则观测自回归（iAR）模型。 通过蒙特卡罗实验评估了所提出方法的估计精度。 得到的结果表明，所提出的在线估计方法能够对生成数据的参数进行精确估计，无论是规则观测还是不规则观测的时间序列。 这些在线方法在数值上是高效的，允许显著的计算时间节省。 此外，我们展示了所提出的方法能够在时间序列行为变化时快速调整参数估计，这与批量估计方法不同。 显示英文摘要

摘要： In the last decades, due to the huge technological growth observed, it has become increasingly common that a collection of temporal data rapidly accumulates in vast amounts. This provides an opportunity for extracting valuable information through the estimation of increasingly precise models. But at the same time it imposes the challenge of continuously updating the models as new data become available. Currently available methods for addressing this problem, the so-called online learning methods, use current parameter estimations and novel data to update the estimators. These approaches avoid using the full raw data and speeding up the computations. In this work we consider three online learning algorithms for parameters estimation in the context of time series models. In particular, the methods implemented are: gradient descent, Newton-step and Kalman filter recursions. These algorithms are applied to the recently developed irregularly observed autoregressive (iAR) model. The estimation accuracy of the proposed methods is assessed by means of Monte Carlo experiments. The results obtained show that the proposed online estimation methods allow for a precise estimation of the parameters that generate the data both for the regularly and irregularly observed time series. These online approaches are numerically efficient, allowing substantial computational time savings. Moreover, we show that the proposed methods are able to adapt the parameter estimates quickly when the time series behavior changes, unlike batch estimation methods.