Statistical Methods for Bounded Time Series Data

• Activity Number: 507 - Business, Time Series, and Spatial Analysis Methods
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Transportation Statistics Interest Group
• Author(s): Michael Bishop* and Jeffrey D. Dawson
• Companies: University of Iowa and University of Iowa College of Public Health, Department of Biostatistics
• Keywords: ARIMA; Frequentist Model; Bayesian Model; Lateral Acceleration; Lane Position; Driving Models

Abstract

Bounded time series data is a unique data structure in which some form of bound exists which encourages individual observations to fall within a specified range. While one could imagine different types of bounds, we focus on a structure in which boundaries, while not strict, do exert some form of pressure on the range of the observations. We examine this structure from both the Frequentist and Bayesian paradigms. We motivate these methods with examples of lane position data from roads with reflective lane boundaries obtained from Alzheimer patients and controls via driving simulator. As Alzheimer patients tend to exhibit different driving patterns than those without the disease, these methods were evaluated based on their ability to distinguish between those with and without the disease. Methods include utilizing traditional ARIMA models while including a signed error term, related to an individual driver’s natural lane position and driving tendencies as outlined in Dawson, et al. (2010). Bayesian and Frequentist paradigms offer attractive features, and both are applicable to such settings. We succeeded in distinguishing between patient groups when using the Bayesian approach.