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

In a previous paper, we 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. In this paper, we carry out an asymptotic analysis of the BSEA for Gaussian AR models. In particular, from a central limit theorem, we obtain expressions for the asymptotic covariances of the parameter estimates. From this we 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 our theoretically predicted parameter estimate covariances are extremely accurate. In addition, we present examples of our order estimation algorithm.