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Asymptotic Nonparametric Statistical Analysis of Stationary Time Series

Part of the SpringerBriefs in Computer Science Book Series

DOI: 10.1007/978-3-030-12564-6

ISBN: 978-3-030-12563-9

Publisher: Springer International Publishing - Springer Journals

Mar 8, 2019

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Introduction

Ryabko, Daniil

Pages: 1 –8

[This chapter is introductory. It discusses the general question of selecting a model for a problem of statistical inference, and motivates the choice of the assumption of stationarity. This and other related models considered in the literature are discussed and compared. Furthermore, a general...
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Preliminaries

Ryabko, Daniil

Pages: 9 –12

[This chapter introduces the notation and definitions necessary for the rest of the book. In particular, stationarity, ergodicity and the distributional distance are defined, with the latter discussed in some detail.]
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Basic Inference

Ryabko, Daniil

Pages: 13 –28

[This chapter considers some basic problems of statistical inference that underly the rest of the problems addressed in this volume. Namely, it is shown how to construct consistent estimates of a distance between stationary ergodic process distributions. As an easy application of this...
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Clustering and Change-Point Problems

Ryabko, Daniil

Pages: 29 –44

[This chapter is devoted to the problems of time-series clustering and change-point analysis. Clustering is grouping together samples generated by the same distributions, while change-point problems are concerned with delimiting parts of a sample that are generated by a different process...
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Hypothesis Testing

Ryabko, Daniil

Pages: 45 –67

[Given a sample from a stationary ergodic distribution, it is required to tell whether the distribution belongs to a set H0 or to a set H1. This general formulation encompasses a variety of problems, including model verification, such as testing that a process is Markov versus it is stationarity...
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Generalizations

Ryabko, Daniil

Pages: 69 –74

[This chapter considers various generalizations of the results surveyed in this volume, as well as some open problems. In particular, generalizations to distances other than the distributional distance are considered, as well as non-stationary processes and processes more general than time...

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