Show that the auto covariance function of an ARMA (1, 1) model, Xt = φXt−1 + Zt +θZt−1, is given by Let {Yt , t ∈ Z} be a weakly stationary process with spectral density f such that 0 ≤ m ≤ f(λ) ≤ M ∈...

Show that the auto covariance function of an ARMA (1, 1) model, Xt = φXt−1 + Zt +θZt−1, is given by

Let {Yt , t ∈ Z} be a weakly stationary process with spectral density f such that 0 ≤ m ≤ f(λ) ≤ M <>∈ [−π,π]. For n ≥ 1, denote by Γn the covariance matrix of [Y1,...,Yn] 0 . Show that the eigenvalues of Γn belong to the interval [2πm,2πM].