Simulate Hover using jQuery

I would use setInterval and jQuery.trigger('mouseover', …).

#MB .list a:hover,
#MB .list a:focus,
#MB .list .active a {
  /* hover styles */
}

(I've simplified your selectors a bit, I would also suggest trying to remove the outer div as these are often unnecessary and the ul alone is enough)

Javascript hover:

function setHover() {
    if ($('#MB .list .active').next().length) {
        $('#MB .list .active').next().addClass('active').end().removeClass('active');
    } else {
        $('#MB .list .active').removeClass('active');
        $('#MB .list li:first-child').addClass('active');
    }
}

setInterval(setHover, 1000);