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.