Due to the introduction of the information criterion AIC and development of prac tical use of Bayesian modeling, the method of time analysis is now showing remarkable progress. In attempting the study of a new field the actual phenomenon is rarely so simple as to allow direct applications of existing methods of analysis or models. The real thrill of the statistical analysis lies in the process of developing a new model depending on the purpose and the characteristics of the object of the research. The purpose of this book ist.o introduce the readers to successful applications of the meth ods of time series analysis in a variety of fields, such as engineering, earth science, medical science, biology, and economics. The editors have been aware of the importance of cooperative research in sta tistical science and carried out various cooperative research projects in the area of time series analysis. The Institute of Statistical Mathematics was reorganized as an inter-university research institute in 1985 and the activities of the Institute have been organized to promote the cooperative researches as its central activity. This book is composed of the outcomes of cooperative researches developed within this environ ment and contains the results ranging from the pioneering realizations of statistical control to the latest consequences of time series modeling.