Inference for μ, γ and F

  • Jan Beran
Chapter

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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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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