A Levinson-Type Algorithm for Modeling Fast-Sampled Data

The standard discrete-time autoregressive model is poorly suited for modeling series obtained by sampling continuous-time processes at fairly rapid rates. Large computational errors can occur when the Levinson algorithm is used to estimate the parameters of this model, due to the ill-conditioning of the Toeplitz covariance matrix to be inverted. An alternative model is developed based on an incremental difference operator rather than the shift operator. It is shown that, as the sampling period goes to zero, unlike the standard AR parameters, the coefficients of this model converge to certain parameters that depend directly on the statistics of the continuous-time process. A Levinson-type algorithm for efficiently estimating the parameters of this model is derived. Numerical examples are given to show that, when the sampling interval is small, this algorithm is considerably less sensitive to arithmetic roundoff errors than the Levinson algorithm.