Series of Irregular Observations

At the university level, in probability and statistics departments or electrical engineering departments, this book contains enough material for a graduate course, or even for an upper-level undergraduate course if the asymptotic studies are reduced to a minimum. The prerequisites for most of the chapters (l - 12) are fairly limited: the elements of Hilbert space theory, and the basics of axiomatic probability theory including L 2-spaces, the notions of distributions, random variables and bounded measures. The standards of precision, conciseness, and mathematical rigour which we have maintained in this text are in clearcut contrast with the majority of similar texts on the subject. The main advantage of this choice should be a considerable gain of time for the noninitiated reader, provided he or she has a taste for mathematical language. On the other hand, being fully aware of the usefulness of ARMA models for applications, we present carefully and in full detail the essential algorithms for practical modelling and identification of ARMA processes. The experience gained from several graduate courses on these themes (Universities of Paris-Sud and of Paris-7) has shown that the mathematical material included here is sufficient to build reasonable computer programs of data analysis by ARMA modelling. To facilitate the reading, we have inserted a bibliographical guide at the end of each chapter and, indicated by stars (* ... *), a few intricate mathematical points which may be skipped over by nonspecialists.