how do I bake an animated sky box using cycles? I would like to turn a specific blender scene into an animated sky box I can use in other animations.

This old tutorial is the top google search result for "blender sky box", but it's for an old version of blender, and some of the buttons it references no longer exist.

There are several tutorials on how to set the sky box if you already have an image, but I have yet to find a modern HOWTO that lays out how to create the sky box image from a scene.  How do I accomplish this?  Keep in mind I want it to be animated, so I'll need to bake a hundred frames or so.
In newer builds of blender, there is a third option in the camera tab for Panoramic. In cycles there is an option for Equirectangular mapping. The output render can then be used as any other sky dome would be used.

Here are the settings: