Generalized heteroskedasticity ACF for moving average models in explicit forms

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 (wi,wj)=∑ with σi,j≠0∀ i ≠ j. secondly: when the diagonal elements of ∑ are not all identical butσi,j = 0 ∀ i ≠ j,i.e.∑=diag(σ11 σ22,σtt). the forms of the explicit equations depend essentially on the moving average coefficients and covariance structure of the disturbance terms.