Exact Discrete Time Representation of Non-stationary Continuous Time Systems with Unequally Spaced Data
This paper presents an exact discrete time representation of non-stationary continuous time systems with unequally spaced flows and mixed stocks and flows. The approach to obtain the exact discrete time representation with flow variables does not depend on the continuous time parameter matrix being non-singular, namely the underlying continuous time system may be non-stationary. In both cases the exact discrete time representations follow a VARMA(1, 1) process with time-varying parameters and heteroskedasticity, despite that the underlying continuous time model has constant parameters and homoskedasticity. The time-varying parameters and the heteroskedastic variance arise due to the variations
in the sampling intervals, whereas the moving average disturbances arise due to the flow nature of the observations. A Monte Carlo simulation on estimation of a cointegrated continuous time system with unequally spaced flows is conducted, aiming at assessing estimate properties when unequal sampling intervals are correctly accounted for. Simulation evidence indicates the favour of exact discrete time models accounting for the irregularity of sampling intervals.
This paper presents an exact discrete time representation of non-stationary continuous time systems with unequally spaced flows and mixed stocks and flows. The approach to obtain the exact discrete time representation with flow variables does not depend on the continuous time parameter matrix being non-singular, namely the underlying continuous time system may be non-stationary. In both cases the exact discrete time representations follow a VARMA(1, 1) process with time-varying parameters and heteroskedasticity, despite that the underlying continuous time model has constant parameters and homoskedasticity. The time-varying parameters and the heteroskedastic variance arise due to the variations
in the sampling intervals, whereas the moving average disturbances arise due to the flow nature of the observations. A Monte Carlo simulation on estimation of a cointegrated continuous time system with unequally spaced flows is conducted, aiming at assessing estimate properties when unequal sampling intervals are correctly accounted for. Simulation evidence indicates the favour of exact discrete time models accounting for the irregularity of sampling intervals.