The invariance and covariance of extracted features from an object under certain transformation play quite important roles in the fields of pattern recognition and image understanding. For instance, in order to recognize a three dimensional object, we need specific features extracted from a given object. These features should be independent of the pose and the location of an object. To extract such features, the authors have presented the three dimensional vector autoregressive model (3D VAR model). This 3D VAR model is constructed on the quarternion, which is the basis of SU(2) (the rotation group in two dimensional complex space). Then the 3D VAR model is defined by the external products of 3D sequential data and the autoregressive (AR) coefficients, unlike the conventional AR models. Therefore the 3D VAR model has some prominent features. For example, the AR coefficients of the 3D VAR model behave like vectors under any three dimensional rotation. In this paper, we present an effective straightforward algorithm to obtain the 3D VAR coefficients from lower order to higher order recursively.