Estimation of Cointegrated Systems in Continuous Time

In this thesis we derive exact discrete time representation models that correspond to cointegrated systems in continuous time. At the same time, for the parameters of those models, estimation procedures are outlined. The representations are applicable for data observed as both stock or flow variables and with the use of some simulated data, the performance of the estimation procedure is assessed. More importantly, with the aim of analysing the costs, if there are any, of ignoring aggregation in the specification, the results of our estimation procedure are also compared with the ones we would have obtained by applying instead Johansen’s estimation methodology. In the first part (Chapter 2), we detail the analysis for a first- order stochastic differential equation system, as a result, baseline finding are outlined. In the second part (Chapter 3) the analysis is generalized and not only includes higher order specifications in the system but also incorporates deterministic components on it. Finally, in the last part (Chapter 4) of this thesis, three applications of that estimation procedure are presented. In the results, when the system is entirely comprised by stock variables and the specification follows a first order system, both Johansen’s methodology and ours perform very well, with virtually identical estimates and, for the simulated data, improvements as the sample size increases. However, when the variables of interest are flows or the specification follows a higher order system, given that our exact discrete time representation includes moving average components in the error term, Johansen’s estimates show a persistent bias in estimation, consequently, they reflected the cost of ignoring aggregation in the specification.