Asymptotic Nonparametric Statistical Analysis of Stationary Time Series

  • Daniil Ryabko

Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Daniil Ryabko
    Pages 1-8
  3. Daniil Ryabko
    Pages 9-12
  4. Daniil Ryabko
    Pages 13-28
  5. Daniil Ryabko
    Pages 29-44
  6. Daniil Ryabko
    Pages 45-67
  7. Daniil Ryabko
    Pages 69-74
  8. Back Matter
    Pages 75-77

About this book


Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus  a rather attractive assumption to base statistical analysis on, especially for problems for which less general qualitative assumptions, such as independence or finite memory, clearly fail. However, it has long been considered too general to be able to make statistical inference. One of the reasons for this is that rates of convergence, even of frequencies to the mean, are not available under this assumption alone.  Recently, it has been shown that, while some natural and simple problems, such as homogeneity, are indeed provably impossible to solve if one only assumes that the data is stationary (or stationary ergodic), many others can be solved with rather simple and intuitive algorithms. The latter include clustering and change point estimation among others. In this volume these  results are summarize.  The emphasis is on asymptotic consistency, since this the strongest property one can obtain assuming stationarity alone. While for most of the problem for which  a solution is found this solution is algorithmically realizable, the main objective in this area of research, the objective which is only partially attained, is to understand what is possible and what is not possible to do for stationary time series. The considered problems include homogeneity testing (the so-called two sample problem), clustering with respect to distribution, clustering with respect to independence, change point estimation, identity testing, and the general problem of composite hypotheses testing. For the latter problem, a topological criterion for the existence of a consistent test is presented.  In addition, a number of open problems is presented.


stationary time series ergodicity time series asymptotic nonparametric

Authors and affiliations

  • Daniil Ryabko
    • 1
  1. 1.Fishlife ResearchBelize CityBelize

Bibliographic information

  • DOI
  • Copyright Information The Author(s), under exclusive license to Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science Computer Science (R0)
  • Print ISBN 978-3-030-12563-9
  • Online ISBN 978-3-030-12564-6
  • Series Print ISSN 2191-5768
  • Series Online ISSN 2191-5776
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