Question

How can i determine the value is changed in the select box without clicking the select box itself.

My code is as follows:

JQUERY

            $("select").each(function() {
                $(this).change(function() {
                    if ($(this).val() === "-Select-"){
                        this.parent().addClass("highlightSelect");
                        this.parent().sibling().show();
                    }   else{
                        this.parent().removeClass("highlightSelect");
                        this.parent().sibling().hide();
                    }
                });
            });

HTML

<div id="wwctrl_add_savedAddressId" class="wwctrl styled-select">
<select id="add_savedAddressId" class="storedPaymentInput_size4 required savedAddress checkDropdown valid" onchange="changeSavedAddressType();generateSavedAddressAdd();" name="summaryData.usedAddress">
<option value="-Select-">-Select-</option>
<option value="O">Enter New Address</option>
<option value="3041">Home - 116 Parrot...</option>
<option value="22268">Other - rwara, aw...</option>
<option value="21372">Other - 1040..</option>
</select>
</div>
<div class="error" for="add_savedAddressId" generated="true" style="display: none;"> Select item</div>

Note: I have other buttons which affects the change of the value of the above select box

Answer 1

First – your code in question will not work.
It must be like this:

                $("select").change(function() {
                    if ($(this).val() === "-Select-"){
                        $(this).parent().addClass("highlightSelect");
                        $(this).parent().siblings().show();
                    }   else{
                        $(this).parent().removeClass("highlightSelect");
                        $(this).parent().siblings().hide();
                    }
                });

parent is jquery object function and not dom object function and this is a dom object which could be turned to jq object like this: $(this). Also, thers is not sibling method in jquery, but there is siblings. Or, if you want to take next/previous sibling you can use .next()/.prev() instead of siblings which will return all siblings of an element

I removed each, but actually that is not required. You may use it, but almost any jquery method will do an operation with set of methods, so $("select") may find few selects in page and $("select").change(...) will bind onchanged handler to all selects found by $("select").

And answerign your question: as I understand you want to call change handler after selected value is changed porgrammatically. You can do that like this: $("select").change(), but this way you will call change event on all selects, so you can do it like this: $("#add_savedAddressId").change(). In second case you will call a change even handler only for select with id add_savedAddressId