Berry-Esseen theorems for quadratic forms of Gaussian stationary processes (Q1062347)

Let \(X_ 1,X_ 2,..\). be a Gaussian stationary process with spectral density f(\(\lambda)\), and let \[ Z_ j=T^{-1/2}\{\sum^{T- j+1}_{\ell =1}(X_{\ell}X_{\ell +j-1}-EX_{\ell}X_{\ell +j- 1})\},\quad j=1,...,p. \] The present paper gives a Berry-Esseen type theorem for the joint distribution of \((Z_ 1,...,Z_ p)\).