Asymptotic normality of cumulant spectral estimates (Q753370)

Let \(\{X_ t\}\), \(t=...-1,0,1,..\). be a stationary strong mixing process with E \(X_ t=0\), f(\(\lambda\)) be the cumulant spectral density of order s of the process \(X_ t\), and \(f_ n(\lambda)\) the cumulant spectral estimate of the density f(\(\lambda\)). The asymptotic normality of \(f_ n(\lambda)\) as \(n\to \infty\) is proved.