Adding an HD Youtube video to the header as default

Hello everyone, I have a small question, and your assistance with it would be greatly appreciated. Does anyone know how could I possibly add a Youtube video in HD to the header section? From what I've noticed the default resolution is either 360p or 480p, which makes my video look pixelated and overall unappealing. It also does not change according to your internet connection like it does on Youtube. Is there a way I could embed the video as a default HD into the header through perhaps a similar way as using links like these www.youtube.com/embed/V1234567?vq=hd1080, or any other way for that matter? By the way, that type of link with the embed is not valid according to the customizer, and also my video is 1920x689, just like the requirements stated. Thank you!