Motion coherence index is a metric to evaluate the coherent motion among vectors. In this article, we propose a coherent motion indicator to describe coherent motion among four adjacent vectors. For the preliminary investigation on stationarity of dynamic texture, the coherent motion indicator is proposed as an attribute of vector. The coherent motion indicator is calculated by averaging the angular distances of four adjacent vectors. Motion coherence index is computed as an average of coherent motion indicators in a video frame. The stationarity is evaluated through the covariance stationary series of motion coherence index in a video scene. Our experiments show that, there is significant difference between dynamic fire texture and dynamic smoke texture, evaluated by that covariance stationary series. Fire textures preserve their covariance stationary series. Conversely, smoke textures demonstrate their covariance non-stationary series. The difference among covariance stationary series models is useful and can be defined as a distinct characteristic among dynamic fire textures and dynamic smoke textures. Consequently, such difference can be brought to leverage in several disciplines of computer vision involved with dynamic textures, such as dynamic texture synthesis and fire calamity surveillance system.