get ‘archive’ of post category

Is it possible to limit the code below to posts of a specific category (and its children)?

$my_archives=wp_get_archives(array(
	'type'=>'monthly', 
	'show_post_count'=>true, 
	'limit'=>20, 						 
        'post_type'=>'post', 
	'format'=>'html' 
));

I’ve got some posts of a certain category ‘my_parent_category’ and am trying to display a monthly archive listing of that particular category (and its children). I’m trying to do it on: category-my_parent_category.php template.

Please advise. Thank you