Statistical analysis of the least squares autoregressive estimator in the presence of noise

This paper analyzes the asymptotic statistical properties of the least squares autoregressive (AR) estimator in the presence of noise. The asymptotic covariance of this estimator is derived for an AR signal with additive white or colored noise. The result is shown to hold for a general (Gaussian or linear) stationary measurement. The analysis is applied in detail to first-order systems. A procedure for using the result to solve problems in speech recognition, biomedical diagnosis, and fault detection is presented. Results of simulations confirm the theoretical analysis.