Variance expressions for spectra estimated using auto-regressions

An expression for the variance of the estimated spectrum based on auto-regressions is developed. This expression is asymptotic in the number of data, but exact in the model order. As the order tends to infinity it converges to the well known result that the variance is proportional to the model order times the square of the spectrum itself. The exact expression gives insight into the character of this convergence, its speed and its dependence on the poles of the underlying AR-process.