Sequential Detection Procedures for Autoregressive Processes

The problem of monitoring the mean (or other aspect) of an evolving time series for deviations from some ideal state arises frequently in such fields as industrial quality control, clinical trials and air (or other) pollution monitoring. This so-called sequential detection problem has been widely studied in the case where the time series consists of independent random variables, a situation which rarely occurs in practice. Little work has been done to develop statistical procedures, called sequential detection procedures (SDP's), to handle such problems under less restrictive assumptions than independence. With this motivation, SDP's are developed for monitoring the parameters of a time-dependent autoregressive model, which is capable of representing the correlation structure of many series encountered in practice, and which can be parameterized so that its parameters represent aspects of a series of typical interest (e.g., its mean or variance). Thus, by monitoring the (time-dependent) parameters, the aspects of interest can be monitored. Two different ways of monitoring the parameters are considered: in the first for deviations from specified target values, in the second for deviations from their unknown values at the beginning of the series. For each way, SDP's for monitoring any subset of the parameters are developed, so that any combination of aspects, such as the mean only, or the variance only, or both the mean and the variance together, may be monitored. iv The SDP's developed consist of repeated tests based on score statistics defined with respect to a likelihood obtained from the autoregressive model. Large sample sequential methodology, based on invariance principles obtained by exploiting the martingale structure of the score statistics, is used to control the false signal rates, and assess the reaction quickness under local alternatives, of the proposed SDP's. Simulation is used to assess reaction quickness under non-local alternatives. Finally, the proposed SDP's are applied to two time series of quality control data from Lipid Research Clinics Laboratories ~o monitor for a shift in mean. Techniques for checking for autore-gressive structure and assessing its order are illustrated. Acknowledgements I wish to express my deep appreciation to my adviser, Professor Pranab Kumar Sen, for his patience, encouragement and invaluable advice in guiding me through this research. I also wish to thank the other members of my committee, Professors J. As my research adviser on the Lipids Project, he contributed significantly to my education as an applied statistician and took a sincere interest in my …