You have two issues in your code.. First you need reference to capture the element on click. Try adding another parameter to your function to reference this. Also active class is for li element initially while you are tryin to add it to "a" element in the function. try this..
<div class="row" style="padding-left:21px;">
<ul class="nav nav-tabs" style="padding-left:40px;">
<li class="active filter"><a href="#month" onclick="Data('month',this)">This Month</a></li>
<li class="filter"><a href="#year" onclick="Data('year',this)">Year</a></li>
<li class="filter"><a href="#last60" onclick="Data('last60',this)">60 Days</a></li>
<li class="filter"><a href="#last90" onclick="Data('last90',this)">90 Days</a></li>
</ul>
</div>
<script>
function Data(string,element)
{
//1. get some data from server according to month year etc.,
//2. unactive all the remaining li's and make the current clicked element active by adding "active" class to the element
$('.filter').removeClass('active');
$(element).parent().addClass('active') ;
}
</script>