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Introduction

  • Jan Beran
Chapter

Abstract

Let \(k\in \mathbb {N}\), \(T\subseteq \mathbb {R}\). A function
$$\displaystyle{x:T\rightarrow \mathbb {R}^{k}\text{, }t\rightarrow x_{t}}$$
or, equivalently, a set of indexed elements of \(\mathbb {R}^{k}\),
$$\displaystyle\left \{ x_{t}|x_{t}\in \mathbb {R}^{k},t\in T\right \}$$
is called an observed time series. We also write
$$\displaystyle{x_{t}\text{ (}t\in T\text{) or }\left ( x_{t}\right ) _{t\in T}.}$$

References

  1. Cantelli, F. P. (1933). Sulla determinazione empirica delle leggi di probabilità. Giornale dell’Istituto Italiano degli Attuari, 4, 421–424.Google Scholar
  2. Glivenko, V. (1933). Sulla determinazione empirica delle leggi di probabilità. Giorn. Ist. Ital. Attuari, 4, 92–99.Google Scholar
  3. van der Vaart, A. W. (1998). Asymptotic statistics. Cambridge: Cambridge University Press.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Jan Beran
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany

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