Asymptotic distribution of spectral estimates of Ito-Wiener integrals (Q1057584)

Let \(\xi_ t\), \(t\in {\mathbb{Z}}\), be a stationary sequence expressed as an n-tuple Ito-Wiener integral with respect to random spectral measure of stationary Gaussian process \(X_ t\). It is assumed that \(X_ t\) has bounded spectral density and the weight function \(\phi\) in the expression of \(\xi_ t\) belongs to \(L_ 4([-\pi,\pi]^ n)\). The asymptotic normality of the spectral estimates of \(\xi_ t\) is proved. The case \(\xi_ t=H(X_ t)\), where \(H: R^ 1\to R^ 1\) is a given function, is also considered. Similar problems were considered earlier by R. Bentkus, G. Maruyama, I. Zhurbenko.