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When the bispectrum is real-valued

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  • Iglói, E.
  • Terdik, Gy.

Abstract

Let {X(t),t∈Z} be a stationary time series with a.e. positive spectrum. Two consequences of that the bispectrum of {X(t),t∈Z} is real-valued but nonzero are: (1) if {X(t),t∈Z} is also linear, then it is reversible; (2) {X(t),t∈Z} cannot be causal linear. A corollary of the first statement: if {X(t),t∈Z} is linear, and the skewness of X(0) is nonzero, then third order reversibility implies reversibility. In this paper the notion of bispectrum is of a broader scope since we do not assume the absolute summability of the third order cumulants.

Suggested Citation

  • Iglói, E. & Terdik, Gy., 2014. "When the bispectrum is real-valued," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 1-5.
    • Handle: RePEc:eee:stapro:v:95:y:2014:i:c:p:1-5
    DOI: 10.1016/j.spl.2014.08.004
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    References listed on IDEAS

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    1. Hinich , Melvin J. & Rothman, Philip, 1998. "Frequency-Domain Test Of Time Reversibility," Macroeconomic Dynamics, Cambridge University Press, vol. 2(1), pages 72-88, March.
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