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

We prove mixing convergence of 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.