Estimation of the Parameters in Stationary Autoregressive Processes after Hard Limiting

Abstract Estimates of the parameters in normal autoregressive (AR(p)) processes may be obtained as functions of certain runs and subsequences in the associated clipped 0 − 1 processes. For example, the parameter in AR (1) is a function of the number of 1 runs only. Equivalently, this parameter can be estimated by counting only the number of axis crossings by the process. The estimates are obtained by a modification of the likelihood function of the clipped data. The loss of information because of hard limiting results in a loss of efficiency relative to the usual maximum likelihood estimates. Nevertheless, for large records our procedure yields quick estimates that do perform well.