Title: Linear stochastic models in discrete and continuous time
Authors: Stephen Pollock - University of Leicester (United Kingdom) [presenting]
Abstract: Statistical time series analysis commonly concerns data sampled at regular intervals from continuously varying signals. The relationships subsisting in the sampled data are usually characterised without reference to the underlying continuous signals. Nevertheless, it is sometimes desirable to attempt to reconstitute the continuous signal from the sampled data by bridging the gaps between the data points. Also, it may be required reconstruct a model of the process generating the data that represents time as a continuum rather than as a sequence of points. Techniques are described that are available for fulfilling these two objectives, and it will place particular emphasis on the correspondence between discrete and continuous models of the same process. It will be shown that the difficulties in establishing a correspondence can often be alleviated by defining a continuous-time forcing function that is bounded infrequency. In that case, there is a one-to-one correspondence between the discrete and the continuous ARMA models. An effective means of establishing a correspondence, when the forcing function is not frequency-limited, will also be demonstrated.