Dynamic textures are sequences of images showing temporal regularity, such as smoke, flames, flowing water, or moving grass. Despite being a multidimensional signal, existing models reshape the dynamic texture into a 2D signal for analysis. In this article, we propose to directly decompose the multidimensional (tensor) signal, free from reshaping operations. We show that decomposition techniques originally applied to study psychometric or chemometric data can be used for this purpose. Since spatial, time, and color information are analyzed at the same time, such techniques permit to obtain more compact models. Only one third or less model coefficients are needed for the same quality and synthesis cost of 2D based models, as illustrated by experiments on real dynamic textures.