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Robust and Nonlinear Time Series Analysis

Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 “Stochastische Mathematische Modelle”, Heidelberg 1983

  • Jürgen Franke
  • Wolfgang Härdle
  • Douglas Martin

Part of the Lecture Notes in Statistics book series (LNS, volume 26)

Table of contents

  1. Front Matter
    Pages N2-IX
  2. Oscar Bustos, Ricardo Fraiman, Victor J. Yohai
    Pages 26-49
  3. M. Deistler
    Pages 68-86
  4. Jürgen Franke, H. Vincent Poor
    Pages 87-126
  5. H. Graf, F. R. Hampel, J.-D. Tacier
    Pages 127-145
  6. E. J. Hannan
    Pages 146-162
  7. R. Douglas Martin, V. J. Yohai
    Pages 198-217
  8. P. Papantoni-Kazakos
    Pages 218-230
  9. P. M. Robinson
    Pages 247-255
  10. P. Rousseeuw, V. Yohai
    Pages 256-272
  11. Back Matter
    Pages 287-287

About these proceedings

Introduction

Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide~sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view be­ cause it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specifica­ tion. They have none-the-less stressed the importance of such optimali­ ty results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assum­ ed model.

Keywords

Analysis Estimator Series Time Time series Variance correlation

Editors and affiliations

  • Jürgen Franke
    • 1
  • Wolfgang Härdle
    • 1
  • Douglas Martin
    • 2
  1. 1.Fachbereich MathematikUniversität FrankfurtFrankfurtGermany
  2. 2.Department of Statistics, GN-22University of WashingtonSeattleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-7821-5
  • Copyright Information Springer-Verlag New York 1984
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96102-6
  • Online ISBN 978-1-4615-7821-5
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site