A noncentral limit theorem for quadratic forms of Gaussian stationary sequences

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 ².