Abstract
We examine the limit behavior of quadratic forms of stationary Gaussian sequences with long-range dependence. The matrix that characterizes the quadratic form is Toeplitz and the Fourier transform of its entries is a regularly varying function at the origin. The spectral density of the stationary sequence is also regularly varying at the origin. We show that the normalized quadratic form converges inD[0, 1] to a new type of non-Gaussian self-similar process, which can be represented as a Wiener-Itô integral onR 2.
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Terrin, N., Taqqu, M.S. A noncentral limit theorem for quadratic forms of Gaussian stationary sequences. J Theor Probab 3, 449–475 (1990). https://doi.org/10.1007/BF01061262
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DOI: https://doi.org/10.1007/BF01061262