论文标题
点过程时间和标记的线性预测
Linear prediction of point process times and marks
论文作者
论文摘要
在本文中，我们对一种特定类型的随机过程的线性预测感兴趣，即标记的时间点过程。观察值是在实际线路上记录的事件时间，每个事件都附加了标记。我们表明，在这种情况下，线性预测从固定随机过程的预测理论直接扩展。遵循经典线条，我们得出Wiener-HOPF型积分方程，以表征线性预测指标，从而扩展了Hawkes过程的“独立起源”（Jaisson，2015）作为推论。我们提出了两种递归方法来解决线性预测问题，并表明这些方法在已知情况下在计算上有效。第一个通过一组微分方程求解Wiener-HOPF方程。它特别适应自回归过程。在第二种方法中，我们开发了一种针对移动平均流程量身定制的创新算法。对两个典型示例的一项小型仿真研究表明，数值方案的应用用于估计霍克斯工艺强度。
In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show that in this case, linear prediction extends straightforwardly from the theory of prediction for stationary stochastic processes. Following classical lines, we derive a Wiener-Hopf-type integral equation to characterise the linear predictor, extending the "model independent origin" of the Hawkes process (Jaisson, 2015) as a corollary. We propose two recursive methods to solve the linear prediction problem and show that these are computationally efficient in known cases. The first solves the Wiener-Hopf equation via a set of differential equations. It is particularly well-adapted to autoregressive processes. In the second method, we develop an innovations algorithm tailored for moving-average processes. A small simulation study on two typical examples shows the application of numerical schemes for estimation of a Hawkes process intensity.
