[devote]

function shiftDays(string, shift) {
    var dt = new Date(string.substr(0, 4), string.substr(4, 2) - 1, string.substr(6));
    var seconds = 1000 * 60 * 60 * 24 * Math.abs(shift);
    dt.setTime(shift >= 0 ? dt.getTime() + seconds : dt.getTime() - seconds);
    var year = dt.getFullYear();
    var month = dt.getMonth() + 1;
    var day = dt.getDate();
    return [
        year,
        (month > 9 ? '' : '0') + month,
        (day > 9 ? '' : '0') + day
    ].join('');
}

alert(shiftDays('20130401', 1));
alert(shiftDays('20130401', -1));