Autoregressive spectral estimators can provide detailed spectral resolution for time series under certain conditions. When a time series includes both an autoregressive process and white noise, a different model is needed. By using higher order Yule-Walker equations, the autoregressive parameters of this type of process can be estimated, resulting in asymptotically multivariate normal estimates. The covariance matrix structure is evaluated for autoregressive-moving average processes and for the specific case of autoregressive plus noise.