Mixing convergence of LSE for supercritical Gaussian AR(2) processes using random scaling

We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical Gaussian autoregressive processes of order 2 having real characteristic roots with different absolute values. We use an appropriate random scaling such that the limit distribution is a two-dimensional normal distribution concentrated on a one-dimensional ray determined by the characteristic root having the larger absolute value.