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Inference for μ, γ and F

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Mathematical Foundations of Time Series Analysis

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Abstract

Assumptions:

$$X_{t}\in \mathbb {R}\text{ (}t\in \mathbb {Z}\text{) weakly stationary, } \mu =E\left ( X_{t}\right )$$
$$\displaystyle f_{X}\left ( \lambda \right ) =\frac {1}{2\pi }\sum _{t=-\infty }^{\infty }e^{-ik\lambda }\gamma _{X}\left ( k\right )$$
$$\displaystyle0<f_{X}\left ( 0\right ) <\infty$$
$$\displaystyle\bar {x}=n^{-1}\sum _{t=1}^{n}X_{t}$$

Then

$$var\left ( \bar {x}\right ) \underset {n\rightarrow \infty }{\sim }2\pi f_{X}\left ( 0\right ) n^{-1}.$$

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany

    Jan Beran

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  1. Jan Beran
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Beran, J. (2017). Inference for μ, γ and F . In: Mathematical Foundations of Time Series Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-74380-6_9

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