A statistical resolution theory of the AR method of spectral analysis

The autoregressive (AR) method of spectral analysis is widely used in diverse areas for its solid theoretical foundation, interesting physical interpretation, computational efficiency, and, more importantly, high resolution capability. Various aspects of its statistical performance have been investigated. However, the resolution probability that provides the most rigorous description of the spectrum resolution capability is still not available in the literature. In this paper, by formulating the resolution event in the framework of statistical decision theory and directly determining its probability from its characteristic function, we obtain an exact asymptotic formula for the probability of resolution. On this basis, we determine the limiting resolving behavior of the sample AR spectrum and develop the corresponding geometrical insight in the parametric space. Simulation and numerical results are also presented to confirm and illustrate the theory