Defining Probability Measures for Time Series

Abstract

Recall:

$$\displaystyle\text{Time series model}=\left ( \varOmega ,\mathcal {F},P\right )$$

$$\displaystyle\varOmega =\left ( \mathbb {R}^{k}\right ) ^{T}=\text{space of functions} \ X:T\rightarrow \mathbb {R}^{k}\text{ (}k\in \mathbb {N},T\subseteq \mathbb {R}\text{)}$$

$$\displaystyle P=\text{probability distribution on}\ \left ( \varOmega ,\mathcal {F}\right )$$