The sample demonstrates how to navigate through the list items using the Keyboard

Tab - Like other widgets, the jqxDropDownList widget receives focus by tabbing into it. Once focus is received, users will be able to use the keyboard to change the selection. A second tab will take the user out of the widget.
Shift+Tab - reverses the direction of the tab order. Once in the widget, a Shift+Tab will take the user to the previous focusable element in the tab order.
Up/Down arrow keys - select previous or next item.
Page Up/Page Down keys - navigate up or down with one page.
Home/End keys - navigate to the first or last item.
Alt Up/Down arrow keys - opens or closes the popup.
Esc - closes the popup.
Enter - selects an item when the popup is opened. Opens the popup when closed.
Incremental Search - start typing to select the matching item.
First letter - press a key to navigate to a matching item. Subsequent press on the same key will iterate over the matches.