Generalized Heteroskedasticity ACF for Moving Average Models in Explicit Forms

Abstract

The autocorrelation function (ACF) measures the correlation between observations at different   distances apart. We derive explicit equations for generalized heteroskedasticity ACF for moving average of order q, MA(q). We consider two cases: Firstly: when the disturbance term follow the general covariance matrix structure Cov(w_i, w_j)=S with s_i,j ¹ 0 " i¹j . Secondly: when the diagonal elements of S are not all identical but s_ij = 0 " i¹j, i.e. S=diag(s₁₁, s_22,…,s_tt). The forms of the explicit equations depend essentially on the moving average coefficients and covariance structure of the disturbance terms.