Unfortenately the combobox feature is poorly documented. You have to visit the example page at
http://jqueryui.com/demos/autocomplete/#combobox and do a view source.
Viewing the source, you will encouter some extra jQuery code that is necessary to run the combobox, starting with
-
function($) {
$.widget("ui.combobox", [...]
Add this code to your project too.
Please note that this extra snippet makes use of the Button widget. When you Build Your Download (to build your UI code) and select "autocomplete" the Button widget is
NOT
automatically selected! Select it yourself!