A continuous time model is, in some ways, more fundamental than a discrete time model. For many variables, the process generating the observations can be regarded as a continuous one even though the observations themselves are only made at discrete intervals. Indeed a good deal of the theory in economics and other subjects is based on continuous time models. There is thus a strong argument for regarding the continuous time parameters as being the ones of interest. This point is argued very clearly in Bergstrom (1976, 1984).

There are also strong statistical arguments for working with a continuous time model. Although missing observations can be handled by a discrete time model, irregularly spaced observations cannot. Formulating the model in continuous time provides the solution. Furthermore, even if the observations are at regular intervals, a continuous time model has the attraction of not being tied to the time interval at which the observations happen to be made.

The aim of the present chapter is to set out the main structural time series models in continuous time. As with any model formulated at a timing interval smaller than the observation interval, it is important to make a distinction between stocks and flows; see section 6.3. Univariate structural models for stock variables are examined in section 9.2 and the relationship between these models and their discrete time counterparts is explored. An important result to emerge from this exercise is that the structure of the two sets of models is very similar.