Estimation of a matrix-valued parameter of an autoregressive process with nonstationary noise

Suppose that $\check{A}_n$ is the least squares estimator constructed from $n$ observations of an unknown matrix $A$ in an autoregressive process $\xi_{k}=A\xi_{k-1}+\varepsilon_{k}$. Under the assumption that the sequence $(\varepsilon_k)$ is a martingale difference, not necessarily stationary and ergodic, we find the limit distribution as $n\to\infty$ of the statistic $\sqrt{n}(\check{A}_{n}-A)$ by using methods of stochastic analysis. This limit distribution may be different from the normal distribution.