Consistent Autoregressive Spectral Estimation for Noise-Corrupted Autoregressive Time Series.

摘要

For the case when the observed series consists of the sum of an autoregressive process of known order and white noise the application of autoregressive spectral estimation methods may not be correct. The presence of the additive noise introduces zeros which are not adequately modeled by an autoregressive model. In this report an autoregressive spectral estimator for the noise-corrupted case is developed and shown to be consistent. The high-order Yule-Walker equations are used to estimate the autoregressive parameters from the noise-corrupted observations. A least squares estimate for the variance of the innovations sequence is also developed and shown to be consistent. These consistent estimates for the autoregressive parameters and the innovations variance are used to form the consistent autoregressive spectral estimates. (Author)