A dynamic skyline query retrieves the moving data objects that are not spatially dominated by any other object with respect to a given query point. Existing efforts on supporting such queries, however, supports location as a single dynamic attribute and one or more static dimensions. In a clear contrast, this paper focuses on the continuous skyline computation on moving data with an arbitrary number of dynamic queriable dimensions, e.g., to model both location and its volatility, with and without static dimension. Toward the goal, we investigate the relative positions and velocities of the initial skyline points with respect to the query, to derive a search region for skyline candidates. After retrieving these candidates, we further prune out some candidates and examine their spatial relations to monitor the changes in the skyline.