Modeling time series data with semi-reflective boundaries

Abstract

Time series data are increasingly common in many areas of the health sciences, and in some instances, may have natural boundaries serving as performance guidelines or as thresholds associated with adverse outcomes. Such boundaries may be labeled as semi-reflective, in that the time series values have an increased chance of returning towards middle levels as the boundaries are approached, but boundaries can still be breached. In this paper we review a model that was previously proposed for such data and we investigate its statistical properties. Specifically, this model consists of a third-order auto-regressive projection component, parameterized as a constrained linear combination of linear, flat, and quadratic trends, and an error term that uses a logistic regression model for its sign. We describe and compare a previously-proposed estimation method with a modified version thereof, using computer simulations, as well as data examples from heart monitoring and from a driving simulator. We find that the two methods tend to give different results, with the modified technique having lower bias and more accurate confidence intervals than the previously-proposed method.

KEYWORDS:

• Driving simulator
• lateral control
• recentering parameter

Acknowledgements

Much of the content of this work was a portion of the lead author's PhD dissertation [8]. We would like to thank the entire neuroergonomics research team in the Department of Neurology at the University of Iowa. We are especially appreciative of our colleagues Joseph Cavanaugh, Matthew Rizzo, Joyee Ghosh, and Gideon Zamba.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Amy M. J. O’Shea http://orcid.org/0000-0003-3272-7952

Additional information

Funding

This work was supported by National Institute of Health (NIH)/National Institute on Aging (NIA) under [grant number AG17177] and [grant number AG15071], and by NIH/National Institute of Neurological Disorders and Stroke (NINDS) under [grant number NS044930].