The Exact Discrete Time Representation of Continuous Time Models with Unequally Spaced Data

This thesis presents the exact discrete time representations of first order continuous time models with unequally spaced stocks, flows and mixed data. With unequally spaced data, given that the underlying continuous time models have constant coefficients and homeskedastic disturbances, the exact discrete time representations exhibit more complicated properties such as time-varying coefficients and heteroskedastic moving average disturbances, which arise due to the irregularity in sampling intervals. When data are purely stock variables, the exact discrete time representation follows a VAR(1) process with time-varying coefficients and serially uncorrelated heteroskedastic disturbances. When data are purely flow variables or a mixture of stocks and flows, the exact discrete time representation follows a VARMA(1, 1) process with time-varying coefficients and moving average heteroskedastic disturbances. Based on unequally spaced real life data, the empirical results show that the parameter estimates are different when accounting for the unequal sampling intervals compared to the approach that assumes data are equally spaced. In addition, the Monte Carlo evidences indicate that there are gains to be made in the estimation, such as smaller estimation bias, when the irregular sampling intervals are correctly accounted for.