  The COVID-19 pandemic in 2020 has caused sudden shocks in transportation
systems, specifically the subway ridership patterns in New York City.
Understanding the temporal pattern of subway ridership through statistical
models is crucial during such shocks. However, many existing statistical
frameworks may not be a good fit to analyze the ridership data sets during the
pandemic since some of the modeling assumption might be violated during this
time. In this paper, utilizing change point detection procedures, we propose a
piece-wise stationary time series model to capture the nonstationary structure
of subway ridership. Specifically, the model consists of several independent
station based autoregressive integrated moving average (ARIMA) models
concatenated together at certain time points. Further, data-driven algorithms
are utilized to detect the changes of ridership patterns as well as to estimate
the model parameters before and during the COVID-19 pandemic. The data sets of
focus are daily ridership of subway stations in New York City for randomly
selected stations. Fitting the proposed model to these data sets enhances our
understanding of ridership changes during external shocks, both in terms of
mean (average) changes as well as the temporal correlations.
