Autoregressive spectral analysis based on statistical autocorrelation

The autoregressive method of spectral analysis is widely used in diverse areas for its solid theoretical foundation. Various aspects of its statistical performance have been investigated. People assume the times series xn to be samples from a zero-mean distribution whose variance remains constant in time. However, it is not available in fact. In this paper, by formulating the resolution event in the framework of statistical autocorrelation theory and directly determining its value from its center-autocorrelation function and statistical autocorrelation function, we obtain a power spectral density formula for the statistical resolution. On this basis, we determine the limiting resolving behavior of the sample autoregressive spectrum and develop the corresponding statistical insight in the time series. Simulation results are also presented to confirm and illustrate the effectiveness of the theory.