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Self-Centering Time Series Data: Single-Pass And Iterative Methods

*Jeffrey D Dawson, University of Iowa College of Public Health 
Amy M Johnson, University of Iowa College of Public Health 

Keywords: Semi-reflective boundaries, Spatial/temporal model, Grid search, Driving studies, Likelihood,

Some time series data have values that tend to reflect back towards the middle of their range, either due to practical boundaries or to central targets. Examples include a motor vehicle being directed back toward the middle of the driving lane as a lane line is approached, a person modifying their exercise pace to maintain a target heart rate, and a health clinic adapting its purchasing to have an ideal amount of supplies in its inventory. Dawson et al (2010) proposed a model to accommodate such boundaries, using third-order polynomial projections with an error term whose sign and magnitude is modeled stochastically. They fit this model using a single pass involving a combination of linear and logistic regression. In this report, we explore iterative likelihood-based methods to fit this model, as well as a modified single-pass method. We do these comparisons use simulated data, as well as vehicular control data from drivers with and without mild Alzheimer’s disease. This work was supported by NIH/NIA awards AG17177 and AG15071.