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In this paper, we investigate the consistency and asymptotic efficiency of anestimator of the drift matrix, $F$, of Ornstein-Uhlenbeck processes that arenot necessarily stable. We consider all the cases. (1) The eigenvalues of $F$are in the right half space (i.e., eigenvalues with positive real parts). Inthis case the process grows exponentially fast. (2) The eigenvalues of $F$ areon the left half space (i.e., the eigenvalues with negative or zero realparts). The process where all eigenvalues of $F$ have negative real parts iscalled a stable process and has a unique invariant (i.e., stationary)distribution. In this case the process does not grow. When the eigenvalues of$F$ have zero real parts (i.e., the case of zero eigenvalues and purelyimaginary eigenvalues) the process grows polynomially fast. Considering (1) and(2) separately, we first show that an estimator, $\hat{F}$, of $F$ isconsistent. We then combine them to present results for the generalOrnstein-Uhlenbeck processes. We adopt similar procedure to show the asymptoticefficiency of the estimator.

Asymptotic Properties of an Estimator of the Drift Coefficients of Multidimensional Ornstein-Uhlenbeck Processes that are not Necessarily Stable