Utilizing ARMA Models for Non-Independent Replications of Point Processes

Mr. Lucas Fellmeth
University of Wisconsin-Milwaukee

The use of a functional principal component analysis (FPCA) approach for estimating intensity functions from prior work allows us to obtain component scores of replicated point processes under the assumption of independent replications. We show these component scores can be modeled using classical autoregressive moving average (ARMA) models, thus allowing us to also apply the FPCA model to non-independent replications. The Divvy bike-sharing system in the city of Chicago is showcased as an application.

Advisor: Prof. Daniel Gervini

Committee Members:
Profs. Daniel Gervini, David Spade, and Chudamani Poudyal