Asymptotic analysis of an algorithm for parameter estimation and identification of 1-b quantized AR time series

Krishnamurthy and Mareels (1995) presented a parameter estimation algorithm called the binary series estimation algorithm (BSEA) for Gaussian autoregressive (AR) time series given 1-b quantized noisy measurements. Of particular interest were the rather surprising computer simulation results that showed that for certain AR series in multiplicative noise, the BSEA based on 1-b quantized measurements yielded significantly better parameter estimates than Yule-Walker methods that are based on the unquantized measurements. The present paper carries out an asymptotic analysis of the BSEA for Gaussian AR models. In particular, from a central limit theorem, the authors 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 1-b quantized measurements and (2) theoretically justify why BSEA can yield better estimates than the Yule-Walker methods in some cases. Computer simulations show that the theoretically predicted parameter estimate covariances are extremely accurate. In addition, the authors present examples of their order estimation algorithm.