Corrigendum to the article “Regular multidimensional stationary time series”

Tamás Szabados

Journal of Time Series Analysis, 2023, vol. 44, issue 3, 331-332

Abstract: In Theorem 2.1 which was the main result of the article it was implicitly assumed that for any regular d‐dimensional weakly stationary time series {Xt} of rank r, 1≤r≤d, there exists an analytic spectral factor Φ(z) of the form Φ(e−iω)=2πU˜(ω)Λr1/2(ω), where Λr(ω) is the r×r diagonal matrix of the positive eigenvalues of the spectral density matrix f(ω) and U˜(ω) is the d×r sub‐unitary matrix of the corresponding eigenvectors. In fact, to the best of my knowledge, it is not known if this assumption is true or false.

Date: 2023
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