Abstract
The paper considers higher-order cumulant spectral estimates obtained by directly Fourier transforming weighted cumulant estimates. Such estimates computationally are different from those based on the finite Fourier transform. These estimates can be looked at continuously as well as directly on submanifolds. The estimates of cumulants are based on unbiased moment estimates. Asymptotic normality is obtained for these estimates and is based on a strong mixing condition and only a finite number of cumulant summability conditions.
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References
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Lii, K.S., Rosenblatt, M. Asymptotic normality of cumulant spectral estimates. J Theor Probab 3, 367–385 (1990). https://doi.org/10.1007/BF01045168
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DOI: https://doi.org/10.1007/BF01045168