I am using SPAutocomplete for a type ahead input text box as shown below. This works great. 

            sourceList: "mySourceList",
            sourceColumn: "mySourceColumn",
            columnName: "DestinationColumn",
            ignoreCase: true,
            numChars: 3,
            slideDownSpeed: 'fast'

I want to write an onChange event on the input text box. Which works only when I type in the input text box and does not work with the autocomplete. I also tried KeyUp, KeyDown, KeyPress - with e=13 which did not work either. 
        $('input[title="DestinationColumn"]').on('change', function () {
           // Logic here            

Finally I am trying to attach the click event to the ul list items that dynamically generate during type ahead. Logic here. This is not working either. 
       $('ul[id^="SPAutocomplete_DestinationColumn"] li').on('click', function () {
           // Logic here

How can I write an onchange event with auto populate select on an input textbox? Any clues will be greatly appreciated. Thank you.