Defining Probability Measures for Time Series

Jan Beran
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Jan Beran: University of Konstanz, Department of Mathematics and Statistics

Chapter Chapter 3 in Mathematical Foundations of Time Series Analysis, 2017, pp 69-100 from Springer

Abstract: Abstract Recall: Time series model = Ω , F , P $$\displaystyle\text{Time series model}=\left ( \varOmega ,\mathcal {F},P\right )$$ time series model Ω = ℝ k T = space of functions X : T → ℝ k ( k ∈ ℕ , T ⊆ ℝ ) $$\displaystyle\varOmega =\left ( \mathbb {R}^{k}\right ) ^{T}=\text{space of functions} \ X:T\rightarrow \mathbb {R}^{k}\text{ (}k\in \mathbb {N},T\subseteq \mathbb {R}\text{)}$$ P = probability distribution on Ω , F $$\displaystyle P=\text{probability distribution on}\ \left ( \varOmega ,\mathcal {F}\right )$$

Date: 2017
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DOI: 10.1007/978-3-319-74380-6_3

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