Asymptotic analysis of an algorithm for identification of quantized AR time-series

Abstract

Krishnamurthy and Mareels presented a parameter estimation algorithm called the binary series estimation algorithm (BSEA) for Gaussian auto-regressive (AR) time series given 1-bit quantized noisy measurements. The present authors carry out an asymptotic analysis of the BSEA for Gaussian AR models. In particular, from a central limit theorem they obtain expressions for the asymptotic covariances of the parameter estimates. From this they: (1) Present an algorithm for estimating the order of an AR series from one-bit quantized measurements. (2) Theoretically they justify why BSEA can yield better estimates than the Yule-Walker methods in some cases.