If state of checkbox was changed can it be permanently saved on page?

If state of checkbox was changed can it be permanently saved on page?

If checkbox was checked/unchacked I want to save its state permanently on
page. I try smth like this:
function saveState() {
document.getElementById($(this).parent().attr('id')).innerHTML =
'<input type="checkbox" checked onclick="saveState.call(this)">'
}
and
<td id="test"> <input type="checkbox" onclick="saveState.call(this)"> </td>
But after page refresh this changes is missed.