Statistical study of reflection coefficients derived from a random AR process

Being linked by non-linear relations, the AR parameters and reflection coefficients cannot both be Gaussian. However, a statistical study can show that these two sets of parameters are Gaussian asymptotically. The aim of this paper is to show that the convergence rate of the reflection coefficient distribution to the Gaussian one depends on the position of the AR model poles in the unit circle. An analysis of the reflection coefficient Taylor expansion around the AR parameters is proposed to determine this convergence rate