Continuous-time autoregressive models: sampling, uniqueness and estimation

Continuous-time autoregressive (AR) models are widely used in astronomy, geology, quantitative finance, control theory and signal processing, to name a few. In practice, the available data is discrete, and one is often required to estimate continuous-time parameters from sampled data. The intertwining relations between the continuous-time model and its sampled version play an important role in such estimation tasks, and this is the main concern of the presented work. In particular, it will be shown that almost every continuous-time AR model is uniquely determined by its sampled version on a uniform grid. This is achieved by removing a set of measure zero from the collection of all AR models and by investigating the asymptotic behaviour of the remaining set of autocorrelation functions. This uniqueness property is further exploited for introducing an estimation algorithm that recovers continuous-time AR parameters from sampled
data, while imposing no constraint on the sampling interval value. The usefulness of the algorithm will be then demonstrated for both Gaussian and non-Gaussian AR processes, as well as for image resizing tasks.

Hagai Kirshner received the B.Sc. (summa cum laude), the M.Sc. and the Ph.D. degrees in electrical engineering from the Technion — Israel institute of Technology, Haifa, Israel in 1997, 2005 and 2009, respectively. He is currently a post-doc fellow at the biomedical imaging group at the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. From 1997 to 2004 he was a system engineer within the Technology Division of the Ministry of Defense. His research interests include sampling theory, biomedical image processing and single molecule localization microscopy.