drupal > views > exposed filter > submit on change

I think this feature works out of the box (at least in Drupal 7). Edit your view and under Exposed form choose

Exposed form style -> Settings

Then there is an option

Autosubmit

where you can choose if you want to "Automatically submit the form once an element is changed". There is also the possibility to use the option

Hide submit button

which is explained by "Hide submit button if javascript is enabled".

@pradeep: you could insert it into a themed view template (see http://www.group42.ca/theming_views_2_the_basics) of your view. (sorry, could not write this as comment according to the forum ui)

In order to have this code re-attached after the ajax call, it should initially be attached via Drupal.behaviors. Something like this:

Drupal.behaviors.myCustomModule = function(context) {
  $('#edit-tid', context).change(function(){
    $('#views-exposed-form-MYVIEW-page-1').submit();
  });
}

Note that the context argument is passed into the selector. Drupal.behaviors should get called again on the new content loaded via ajax.

Update: I didn't notice you were inserting the js via the views footer. The above should still work, just replace 'myCustomModule' with some unique identifier so you don't override other behaviors.