Time series analysis

Preface The course Time series analysis is based on the book [7] and replaces our previous course Stationary stochastic processes which was based on [6]. The books, and by that the courses, differ in many respects, the most obvious is that [7] is more applied that [6]. The word " applied " is partly a fine word for " elementary ". A very important part of the course consists in looking at and thinking through the examples in [7] and to play around with the enclosed computer package ITSM or with Matlab. Jan Enger has constructed a number of M-files in order to facilitate use of Matlab within this course. Those who want to use Matlab later in connection with time series can use the toolbox System Identification by Lennart Ljung, which contains an extensive library of stochastic models related to time series and control theory. The main reason for the change in the courses is that half of our intermediate course Probability theory treats stationary processes from a theoretical point of view. A second reason is that a course in time series analysis is useful also for students more interested in applications than in the underlying theory. There are many references to [6] in [7] and the best recommendation to give a student interested in the subject also from a more theoretical point of view is to buy both books. However, due to the price of books, this recommendation might be unrealistic. A " cheaper " recommendation to those students is to read this lecture notes, where many parts from our previous course, i.e. in reality from [6], are included. These parts are given in the Appendix and in inserted paragraphs. The inserted paragraphs are written in this style. I am most grateful for all kind of criticism, from serious mathematical mistakes to trivial misprints and language errors.