Non-Stationary Time Series Model for Station-Based Subway Ridership During COVID-19 Pandemic: Case Study of New York City

Abstract

The COVID-19 pandemic in 2020 has caused sudden shocks in transportation systems, specifically the subway ridership patterns in New York City (NYC), U.S. 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 assumptions might be violated during this time. In this paper, utilizing change point detection procedures, a piecewise stationary time series model is proposed 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 NYC for randomly selected stations. Fitting the proposed model to these data sets enhances understanding of ridership changes during external shocks, both in relation to mean (average) changes and the temporal correlations.

Will transit recover? A retrospective study of nationwide ridership in the United States during the COVID-19 pandemic

“…Stay-at-home orders and higher unemployment rates defined this period. This finding aligns with the findings of prior studies in different regions ( Moghimi et al, 2022 , Osorio et al, 2022 ). The other changepoint in June 2021 signals the beginning of the recovery for transit ridership.…”

“…Changepoints are defined as " abrupt variations in time series data " and could represent changes that occur between conditions or states ( Aminikhanghahi and Cook, 2017 ). Changepoint analysis is gaining interest in the field of transportation in the wake of the COVID-19 pandemic; some recent studies have used this method to explore changes in mobility levels and subway ridership during COVID-19 ( Panik et al, 2022 , Moghimi et al, 2022 ). Changepoint analysis was applied to identify changes in ridership recovery measured as the percent decline compared to the same month in 2019.…”

“…In the United States, several studies have explored the impact of COVID-19 on transit ridership with a focus on a specific city or a specific state like New York City ( Halvorsen et al, 2021 , Wang and Noland, 2021 , Moghimi et al, 2022 ), Chicago ( Hu and Chen, 2021 ), Nashville ( Wilbur et al, 2020 ), Chattanooga ( Wilbur et al, 2020 ), Los Angeles ( Gleason, 2021 ), North Dakota ( Molina et al, 2021 ), and Ohio ( Simons et al, 2021 ). However, a limited number of studies have explored the COVID-19 impacts on transit ridership in more than one region of the United States, which is the focus of the following brief literature review.…”

ARIMA Time Series Modeling with the Addition of Intervention and Outlier Factors on Inflation Rate in Indonesia

“…The Autoregressive Integrated Moving Average (ARIMA) model is a type of ARMA(𝑝, 𝑞) model that includes a non-stationary assumption. This non-stationarity is solved by applying a differencing process, repeated 𝑑 times, until the data meet the stationarity assumption (Moghimi et al, 2023). The model used to write as ARIMA (𝑝, 𝑑, 𝑞) where 𝑝 denotes the autoregressive process, 𝑑 represents the number of differencing and 𝑞 means the moving average process order (Mahia et al, 2019).…”

Development of Accuracy for the Weighted Fuzzy Time Series Forecasting Model Using Lagrange Quadratic Programming

“…The ARIMA model has a limitation, requiring the assumption of stationarity, which means it cannot be directly applied to time series data with a trend pattern (Moghimi et al, 2023). The presence of a trend pattern causes uncertainty in the average value of the time series data.…”