Only fire function when user is done typing

In JavaScript, when you want to set a callback, you need to bind to a function. Assuming you also want to be in the Aura life cycle (which is almost always yes), the resulting Aura version of the code looks like this:

onKeyUpHandler:function(component, event, helper) {
    let timer = setTimeout(
      $A.getCallback(
        helper.handleSearch.bind(helper,component,event,helper)
    ), 1000) 
    component.set("v.timer", timer);
},
onKeyDownHandler:function(component) {
    let timer = component.get("v.timer");
    clearTimeout(timer);
    component.set("v.timer", null);
}

Notable changes:

• v.timer is set to null after clearing the timer.
• v.timer is not read before setting it via setTimeout.
• $A.getCallback ensures you're in an Aura life cycle event.
• .bind(helper, component, event, helper) returns a bound function reference with this set to helper (the same behavior as if you'd called it directly). Without this, the original code was calling the method immediately instead of waiting 1,000 ms.