Asymptotic normality and efficiency of a weighted correlogram - Maiboroda, R. E. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
For a process X(t)=Σ j=1 M g j (t)ξ j (), where gj(t) are nonrandom given functions, \((ξ _j (t),j = 1,M )\) is a stationary vector-valued Gaussian process, Eξk(t) = 0, and Eξk(0) Eξl(τ) = r kl(τ), we construct an estimate \(r_kl (τ ,T)\) for the functions r kl(τ) on the basis of observations X(t), t ∈ [0, T]. We establish conditions for the asymptotic normality of \(T (r_kl (τ ,T) - r_kl (τ ))\) as T → ∞. We consider the problem of the optimal choice of parameters of the estimate \(r_kl \) depending on observations.