Trend and seasonality estimation for point-process time series

2026-05-20

AI Summary

This study addresses the challenge of effectively estimating trend and seasonal components in point process time series by proposing a spatiotemporal doubly stochastic Poisson model based on a log-Gaussian intensity function. The authors develop a computationally efficient M-estimator to jointly extract trend and seasonal patterns, offering the first decomposition framework for irregular event sequences that combines interpretability with theoretical guarantees. They derive the asymptotic distribution of the proposed estimator, establishing its statistical properties. Simulation studies demonstrate favorable finite-sample performance, and the method is successfully applied to Chicago Divvy bike-sharing data, uncovering interpretable spatiotemporal dynamics in user demand.

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.

Problem

• trend estimation
• seasonality estimation
• point-process time series
• doubly-stochastic Poisson model
• log-Gaussian intensity

Innovation

• point-process time series
• doubly-stochastic Poisson model
• log-Gaussian intensity
• M-estimators
• trend and seasonality estimation