Series of Irregular Observations

Forecasting and Model Building

  • Robert Azencott
  • Didier Dacunha-Castelle

Part of the Applied Probability book series (APPLIEDPROB, volume 2)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Robert Azencott, Didier Dacunha-Castelle
    Pages 1-2
  3. Robert Azencott, Didier Dacunha-Castelle
    Pages 3-9
  4. Robert Azencott, Didier Dacunha-Castelle
    Pages 10-17
  5. Robert Azencott, Didier Dacunha-Castelle
    Pages 18-24
  6. Robert Azencott, Didier Dacunha-Castelle
    Pages 25-36
  7. Robert Azencott, Didier Dacunha-Castelle
    Pages 37-45
  8. Robert Azencott, Didier Dacunha-Castelle
    Pages 46-54
  9. Robert Azencott, Didier Dacunha-Castelle
    Pages 55-66
  10. Robert Azencott, Didier Dacunha-Castelle
    Pages 67-82
  11. Robert Azencott, Didier Dacunha-Castelle
    Pages 83-100
  12. Robert Azencott, Didier Dacunha-Castelle
    Pages 101-117
  13. Robert Azencott, Didier Dacunha-Castelle
    Pages 118-140
  14. Robert Azencott, Didier Dacunha-Castelle
    Pages 141-161
  15. Robert Azencott, Didier Dacunha-Castelle
    Pages 162-180
  16. Robert Azencott, Didier Dacunha-Castelle
    Pages 181-222
  17. Robert Azencott, Didier Dacunha-Castelle
    Pages 223-226
  18. Back Matter
    Pages 227-236

About this book

Introduction

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.

Keywords

Estimator Gaussian process Innovation Likelihood Maxima Probability space Random variable best fit ergodicity random measure

Authors and affiliations

  • Robert Azencott
    • 1
  • Didier Dacunha-Castelle
    • 1
  1. 1.Equipe de Recerche Associée au C.N.R.S. 532 Statistique Appliquée MathématiqueUniversité de Paris-SudOrsay CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4912-2
  • Copyright Information Springer-Verlag New York 1986
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-9357-6
  • Online ISBN 978-1-4612-4912-2
  • Series Print ISSN 0937-3195
  • About this book