This article introduces estimators of trend and seasonality for time series of point processes. We assume the point processes follow a temporal or spatial doubly-stochastic Poisson model with log-Gaussian intensity functions. The proposed estimators are computationally simple M-estimators. Their asymptotic distribution is derived, and their finite-sample performance is studied by simulation. As an example of real-data application, we study the patterns of bike demand in the Divvy bike-sharing system of the city of Chicago.

翻译：本文提出了点过程时间序列中趋势和季节性的估计方法。我们假设点过程遵循具有对数高斯强度函数的时间或空间双重随机泊松模型。所提出的估计量是计算简单的M估计量。本文推导了其渐近分布，并通过模拟研究了其在有限样本下的表现。作为真实数据应用的例子，我们研究了芝加哥市Divvy共享单车系统中自行车需求模式。