Dynamical correlations in simple quantum spin models can be conveniently studied via the continued fraction formalism in which the Laplace transformed dynamical two-point correlation can be written as C(z) = 1/(z + Δ1/(z + Δ2/(z + to ∞))), where Δn's are functions of static correlations. Very often, for systems without any natural dominant characteristic frequencies, as n increases, Δn ≊ κnα, α=0 or 1, κ being some constant, for large n for simple quantum spin systems. It is suggested that this property of Δn's could be related to some underlying "nearly noninteracting fermionic nature" of these quantum spin systems.