Statistical properties of AR spectral analysis

This paper investigates several statistical properties of the autoregressive (AR) spectral analysis method by using the periodogram technique recently devised by the author. When the data are made up of several sinusoids contaminated by stationary noise, the asymptotic variances of the AR spectral estimator are given. It is shown numerically that the behavior of the variances is similar to Kromer and Berk's earlier result for stationary processes. As for frequency measurement accuracies, the statistical fluctuation of a peak frequency is analyzed under the assumption that the deviation from the true peak frequency is small. It is shown numerically that the resulting variance is inversely proportional to the data length and the square of the signal-to-noise ratio (SNR).