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Spectral Representation of Univariate Time Series

  • Jan Beran
Chapter

Abstract

$$\displaystyle{X_{t}\text{ second order stationary, } E\left ( X_{t}\right ) =0\text{, } \gamma _{X}\left ( k\right ) =\int _{-\pi }^{\pi }e^{ik\lambda }dF_{X}\left ( \lambda \right )}$$
$$\displaystyle\Rightarrow \text{additive decomposition of }X_{t} \text{ into periodic components?}$$

References

  1. Ash, R. B. (1972). Real analysis and probability. New York: Academic Press.Google Scholar
  2. Brockwell, P. J., & Davis, R. A. (1991). Time series: Theory and methods. New York: Springer.Google Scholar
  3. Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 47, 617–644.Google Scholar
  4. Shannon, C. E. (1948). A mathematical theory of communication. Bell Systems Technical Journal, 27, 379–423.Google Scholar

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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