On model-fitting for fast-sampled data

Summary form only given, as follows. The conventional discrete-time autoregressive model is poorly suited for modeling series obtained by rapidly sampling continuous-time processes. The extreme ill-conditioning of the covariance matrix to be inverted in such cases causes numerical instabilities in the Levinson algorithm for estimating the autoregressive parameters. An alternative model, based on an incremental difference operator rather than the conventional shift operator, has been developed recently by the authors jointly with Goodwin and Moore. As the sampling interval goes to zero, the parameters of this model converge to certain parameters which depend on the statistics of the continuous-time process. A Levinson-type algorithm can be employed for efficiently estimating the parameters of this model. The properties of this and related difference-based algorithms are explored both analytically and numerically.