Monitoring of count data time series: Cumulative sum change detection in Poisson integer valued GARCH models

Abstract

This article presents a cumulative sum (CUSUM) monitoring approach for count-data time series. A seasonal integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH(1,1)) time series model with Poisson deviates is used to develop a likelihood ratio test formulation to detect changes in the process accounting for temporal correlations and seasonality. Simulation studies show that the proposed CUSUM monitoring approach can provide significantly improved performance in applications where serial correlation or seasonality is prevalent. A case study with real traffic crash counts is presented to illustrate the application of the proposed methodology for roadway safety improvement.

Keywords:

• Prospective monitoring
• cumulative sum
• count data time series
• crash data

Acknowledgments

We thank the Florida Department of Transportation for providing the roadway crash data. The opinions, views and findings expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, the US Government, or The Florida Department of Transportation.

Additional information

Notes on contributors

O. Arda Vanli

Omer Arda Vanli is an Associate Professor in the Industrial and Manufacturing Engineering Department at Florida State University and Florida A&M University. Dr. Vanli's research focuses on statistical process monitoring, Bayesian methods, condition monitoring of engineering systems and calibration and validation of computational models. He completed his PhD in Industrial Engineering and Operations Research at the Pennsylvania State University, University Park, PA in 2007. Prior to his PhD he received his BS degree in Mechanical Engineering from the Middle East Technical University, Ankara, Turkey in 1998 and his MS degree in Mechanical Engineering from the Pennsylvania State University, University Park, PA in 2000.

Rupert Giroux

Rupert Giroux currently works as a Public Transportation Specialist in the State Safety Office at the Florida Department of Transportation and he is a PhD candidate in the Industrial and Manufacturing Engineering Department at Florida State University. Mr. Giroux is a Lean Six Sigma Green Belt with several years of industrial experience as a quality engineer. His research concentrates on statistical process monitoring, response surface methodology, and quality and process improvement. Mr. Giroux completed his MS degree in Industrial Engineering from Florida State University in 2001 and his BS degree in Mechanical Engineering from Florida State University in 1997.

Eren Erman Ozguven

Eren Erman Ozguven is an Assistant Professor at the Department of Civil & Environmental Engineering at FAMU-FSU College of Engineering. Dr. Ozguven holds a BSc degree in Civil Engineering from the Bogazici University, Turkey (2002), MSc degree in Industrial Engineering from the Bogazici University, Turkey (2006) and a PhD degree in Civil and Environmental Engineering from the Rutgers University, NJ, USA (2013) with concentration in emergency supply transportation operations. His research interests include smart cities, urban mobility, traffic safety and reliability, emergency transportation, and intelligent transportation systems.

Joseph J. Pignatiello

Joseph J. Pignatiello, Jr. is a Professor of Operations Research and the Head of the Department of Operational Sciences at the Air Force Institute of Technology. He earned his PhD in Industrial and Systems Engineering from The Ohio State University. His research is primarily focused on the areas of statistical process monitoring, design and analysis of experiments, and reliability engineering. He is a Fellow of both the American Society for Quality and the Institute of Industrial and Systems Engineers.