Publ. Math. Debrecen 49 / 3-4 (1996), 211–218 Statistical inference for multidimensional AR processes By (Debrecen) and (Debrecen) Abstract. It is shown that the suitably normalized maximum likelihood estima- tor of some parameters of multidimensional autoregressive processes with coefficient matrix of a special structure have exactly a normal distribution. 1. Introduction Consider the 2–dimensional real–valued stationary autoregressive pro- cess X (t), t ≥ 0, given by the stochastic differential equation (SDE)  dX 1 (t) dX 2 (t) ¶ =  -λ -ω ω -λ ¶ X 1 (t) dt X 2 (t) dt ¶ +  dW 1 (t) dW 2 (t) ¶ , where W (t)=(W 1 (t),W 2 (t)), t ≥ 0, is a standard 2–dimensional Wiener process and λ> 0, ω ∈ R are unknown parameters. This process is a so–called 2–dimensional Ornstein–Uhlenbeck process. Now consider the following statistics: s 2 X (t)= Z t 0 (X 2 1 (u)+ X 2 2 (u))du, r X (t)= Z t 0 (X 1 (u) dX 2 (u) - X 2 (u) dX 1 (u)). As it is known the maximum likelihood estimator (MLE) of the parameter ω is given by b ω X (t)= r X (t) s 2 X (t) , Mathematics Subject Classification : 62M10.