Add video to Home Page Slider

I’d like to use a video (such as an .mp4) instead of static images in the Home Page Slider. Is there any way I could implement this using .PHP or a plugin?

For reference, this is what I have right now: here
And this is what I’d like to have: here

That second link was a pure .PHP version of the site (without WordPress), where we had the following code. Is there somewhere in the theme content that I could simply copy this chunk to? Thank you!

<video src="banner_videos/video1.mp4" autoplay id="backgroundVideo" poster="banner_videos/banner.jpg"></video>
    <script type='text/javascript'>
      var i = 0;
      var videoList = ["banner_videos/video1.mp4", "banner_videos/video2.mp4"]; //,"banner_videos/video2.mp4"];
      var numVideos = videoList.length;

      document.getElementById('backgroundVideo').addEventListener('ended', myHandler, false);

      function myHandler(e) {
        if (!e) {
          e = window.event;
        }
        i++;
        if (i == numVideos) {
          i = 0;
        }
        $('#backgroundVideo').attr("src", videoList[i]);
      }
    </script>