<field
            name="studio_id"
            type="text"
            label="COM_JPANIMES_STUDIO_LABEL"
            description="COM_JPANIMES_STUDIO_DESC"
            size="100"
            class="span5"
            default=""
            />

$( "#jform_studio_id" ).autocomplete({

minLenght:0,

source: function( request, response ) {
                  $.ajax({
                    url : 'index.php?format=raw&option=com_mycomponent&task=testing',
                    dataType: "raw",
                    type: "POST",
                    data: {search: request.term,},

                    success: function( data ) {
                        response( $.map( data, function( item ) {
                            return {
                                label: item.studio_name,
                                studio_id: item.studio_id
                            }
                        }));
                    }
                  });
              },

select: function( event, ui ) {

    $("#jform_studio_id").val(ui.item.studio_id);
},

messages: {
    noResults: '',
    results: function() {}
},

open: function() {
    $("ul.ui-menu").width( $(this).innerWidth() );
}

<?php
defined('_JEXEC') or die('Restricted access');

class JpanimesController extends JControllerLegacy
{
    protected $default_view = 'mycomponent';

    public function testing() {

        $studios[] = array('studio_id' => '1', 'studio_name' => 'studio');

        echo json_encode($studios);
    }
}
?>