Embed videos in widgets not using a video service

What’s up people! I am looking to embed a video using adobe after affects with some motion graphics onto my site. I am looking to be able to embed the effects on site in content side bar area aka via widget. But would like the video to loop.
Can I embed videos of my own without using a service like YouTube? And is there short codes to add to embed videos in widgets with looping. I read on codex about it but dont really understand what I should do. Thanks in advance peeps.