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# A noncentral limit theorem for quadratic forms of Gaussian stationary
sequences

**Norma Terrin
**

Murad S. Taqqu

### Abstract:

*We examine the limit behavior of quadratic forms of stationary Gaussian
sequences with long-range dependence. The matrix which 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 in to a new type of
non-Gaussian self-similar process which can be represented as a Wiener-Itô
integral on .
*