On the asymptotic normality of autoregressive spectral density estimates for the noise corrupted case

Asymptotic statistics for spectral density estimates of noise corrupted autoregressive (AR) series are evaluated. The "high-order" Yule-Walker equation estimates of the autoregressive parameters are used to form a spectral density estimate. The estimate is shown to be a consistent asymptotically normal (CAN) estimate. An expression for the variance of the limiting distribution in terms of the AR process parameters and the noise variance is provided.