Spatio-temporal analysis of public transportation systems using network autoregressive models

Abstract

This research study covers the literature behind statistical spatio-temporal analysis as well as the progress made thus far in exploring its applications in the domain of public transportation. The research project delves into data provided by Open Data NY covering the New York City (NYC) Subway System, making use of statistical methods to accurately forecast future changes.

This analysis showcases the usage and application of the Generalised Network Autoregressive (GNAR) model as proposed by authors Knight and Leeming, to fit a model to predict the ridership of the various subway stations around NYC. Authors Nason and Wei showcased the model’s prowess in the domain of economics by quantifying and predicting the economic response to COVID-19 across various European countries. This paper showcases the GNAR model’s use case in the domain of transport, making use of the subway station’s pre-existing graph network structure to aid in predictions.

As it concludes, the paper would have gone through the steps taken to extract, transform, and load the data making use of Python and the Pandas library. The raw data obtained using the MTA API will be transformed into graphical networks and vector time series’ compatible with the autoregressive model. Subsequent analyses would be conducted in R, outlining the conditions and consolations given to provide a model that would be useful in forecasting. This includes an investigation to the Bayesian Information Criterion (BIC) of each model, observations of its predictive power represented by the mean squared prediction error (MSPE) and explained variance (R-squared) of each model.

The paper also covers several challenges faced during the data exploration of model fitting, offering potential solutions to future renditions of this project. Specifically, improvements to parameter selection and graph network construction have been outlined in the closing review, along with extensions to compare regression-based analyses against machine learning and large language model (LLM) based analyses.