For pattern recognition and image understanding, it is important to take invariance and/or covariance of features extracted from given data under some transformation into consideration. This makes various problems in pattern recognition and image understanding clear and easy. In this article, we present two autoregressive models which have proper transformation properties under rotations: one is a 2D autoregressive model (2D AR model) which has invariance under any 2D rotations and the other is a 3D autoregressive model (3D AR model) which has covariance under any 3D rotations. Our 2D AR model is based on a matrix representation of complex number. It is shown that our 2D AR model is equivalent to Otsu's complex AR model. On the other hand, our 3D autoregressive model is based on the representation theory of rotation group such as the fundamental representation of Lie algebra of SU(2)(Special Unitary group in 2D which includes rotation group), which is called Pauli's matrices.