Monitoring Methods for Time Series & Panel Data Models with Application to Statistical Process Control

Abstract

In this thesis, we study three subjects. The first subject study the monitoring procedure to detect a parameter change in GARCH-type models based on the cumulative sum (CUSUM) of score functions as in Gombay and Serban (2009). For illustration, a simulation study is carried out for asymmetric GARCH models. The second subject examines the statistical process control chart used to detect a parameter shift with Poisson integer-valued GARCH (INGARCH) models and zero-inated Poisson INGARCH models. INGARCH models have a conditional mean structure similar to GARCH models and are well known to be appropriate to analyzing count data that feature overdispersion. Special attention is paid in this study to conditional and general likelihood ratio-based (CLR and GLR) CUSUM charts and the score function-based CUSUM (SFCUSUM) chart. The performance of each of the proposed methods is evaluated through a simulation study, by calculating their average run length. Our _ndings show that the proposed methods perform adequately, and that the CLR chart outperforms the GLR chart when there is an increased shift of parameters. Moreover, the use of the SFCUSUM chart in particular is found to lead to a lower false alarm rate than the use of the CLR chart. Finally, the third subject study methods for monitoring parameter change in Panel data models. Here we establish monitoring methods based on eigenvalue for models. We evaluate the performance of the proposed methods through a simulation study and illustrate some empirical analysis.