Throughout their history, human beings have been fascinated by time. Indeed, what is history but an interpretation of time? Each civilisation has had its own special conception of time. Our present anti-civilisation only knows ‘time is money’! No one can deny that the study of time is important. This text attempts to make more widely available some of the tools useful in such studies.

Thus, my aim in writing this text is to introduce research workers and students to ways of modelling a wide variety of phenomena that occur over time. My goal is explicitly to show the broadness of the field and the many inter-relations within it. The material covered should enable mathematically literate scientists to find appropriate ways to handle the analysis of their own specific research problems. It should also be suitable for an introductory course on the applications of stochastic processes. It will allow the instructor to demonstrate the unity of a wide variety of procedures in statistics, including connections to other courses. If time is limited, it will be possible to select only certain chapters for presentation.

No previous knowledge of stochastic processes is required. However, an introductory course on statistical modelling, at the level of Lindsey (2004), is a necessary prerequisite. Although not indispensable, it may be helpful to have more extensive knowledge of several areas of statistics, such as generalised linear and categorical response models. Familiarity with classical introductory statistics courses based on point estimation, hypothesis testing, confidence intervals, least squares methods, personal probabilities, … will be a definite handicap.

Many different types of stochastic processes have been proposed in the literature. Some involve very complex and intractable distributional assumptions.