On parameter estimation of autoregressive process in the presence of noise

The paper studies the problem of parameter estimation for autoregressive (AR) process in the presence of white observation noise. A new type of bias compensated least-square (BCLS) algorithm is proposed to obtain consistent parameter estimate for AR models. The main feature of the proposed algorithm is that an auxiliary backward output parameter estimator is introduced in order to estimate the variance of observation noise. The proposed algorithm compensates the bias via the estimated variance of observation noise and hence yields a consistent parameter estimate. Some comments are given to illustrate that the proposed algorithm is less computational burden and more mimetically reliable. Numerical results are provided to support these comments.