Introduction

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

$$\displaystyle{x_{t}\text{ (}t\in T\text{) or }\left ( x_{t}\right ) _{t\in T}.}$$