When the bispectrum is real-valued

E. Iglói and Gy. Terdik

Statistics & Probability Letters, 2014, vol. 95, issue C, 1-5

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.

Keywords: Bispectrum; Cumulant; Nonlinearity; Causality; Reversibility (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2014.08.004

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