First you have to inject the filter like this:
app.factory('myService', ['$rootScope', '$filter', function($rootScope, $filter)
(The array is only needed when you use minification in your build process)
To call specific filter programmatically:
$filter('date')(new Date(), 'yyyy-MM-01');
$filter(name)
returns the specific filter function, which you can than call with your arguments:
var dateFilter = $filter('date');
var filteredDate = dateFilter(new Date(), 'yyyy-MM-01')