The exact discrete time representation of a system of fourth-order differential equations

The exact discrete time representations of both a closed and an open system of fourth-order differential equations are considered, in which all vector processes may contain both stock and flow variables. For extra generality, the closed system of equations contains seasonal dummies. The open system here contains levels and derivatives (up to fourth. order) of the vector of exogenous variables whose continuous time paths are approximated using a quartic interpolant.