Summary
Limit theorems with a non-Gaussian (in fact nonstable) limiting distribution have been obtained under suitable conditions for partial sums of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence. Analogous limit theorems are here obtained for finite Fourier transforms of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence.
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Davis, R.A., Lii, KS., Politis, D.N. (2011). Limit Theorems for Fourier Transforms of Functionals of Gaussian Sequences. In: Davis, R., Lii, KS., Politis, D. (eds) Selected Works of Murray Rosenblatt. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8339-8_31
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DOI: https://doi.org/10.1007/978-1-4419-8339-8_31
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