Trend and seasonality estimation for point-process time series

TL;DR

This paper proposes simple M-estimators for extracting trend and seasonality from point-process time series, with theoretical analysis and real-world application to bike-sharing data.

Contribution

It introduces novel, computationally simple estimators for trend and seasonality in doubly-stochastic Poisson point processes, with asymptotic properties and practical validation.

Findings

Estimators are asymptotically normal.

Finite-sample performance is validated via simulation.

Application to Chicago bike demand reveals meaningful patterns.

Abstract

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.