A noncentral limit theorem for quadratic forms of Gaussian stationary sequences |
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Authors: | Norma Terrin Murad S Taqqu |
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Institution: | (1) Department of Mathematics, Boston University, 111 Cummington St., 02215 Boston, Massachusetts |
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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 inD0, 1] to a new type of non-Gaussian self-similar process, which can be represented as a Wiener-Itô integral onR
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Keywords: | Self-similar processes power counting long-range dependence Wiener-Itô integrals |
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