You can use dispatch to send / fire an event for an element: element.dispatchEvent(event);. The support may vary on different browsers and versions; my demo on jsfiddle worked on chrome 65.
This is the demo
function simulateMouseOver() {  
  var item2 = document.querySelectorAll("ul li")[1];
  var event = new MouseEvent('mouseover', 
           {view: window, bubbles: true, cancelable: true});
      
  var cancelled = !item2.dispatchEvent(event);
  if (cancelled) {
        // a handler called preventDefault.
        
  } else {
        // none of the handlers called preventDefault.
  }
}
var menu =  document.getElementById("menu");
menu.addEventListener("mouseover", function(event){   
   event.target.style.backgroundColor = "lime";
   setTimeout(function() { 
            event.target.style.backgroundColor = "";
   }, 800);
}, false);
ul {background-color: lightgray}
<h3>Sample to fire onmouseover using a script</h3>
<ul id="menu">
  <li>one</li>
  <li>two</li>
  <li>three</li>
</ul>
<button onclick="simulateMouseOver()">simulate onMouseOver item two</button>
 
 
The html
<h3>Sample to fire onmouseover using a script</h3>
<ul id="menu">
   <li>one</li>
   <li>two</li>
   <li>three</li>
</ul>
<button onclick="simulateMouseOver()">simulate onMouseOver</button>
Below an onmouseover-event is set for <ul id=menu>. As soon as the mouse is moved over ul or any node inside ul:
var menu =  document.getElementById("menu");
menu.addEventListener("mouseover", function(event){   
     event.target.style.backgroundColor = "blue";
     setTimeout(function() {
          event.target.style.backgroundColor = "";
     }, 500);
}, false)();
To  raise the onmouseover-event from inside a script you
- first have to create the correct event
- an then fire / dispatch this event to the target-element
See this code
function simulateMouseOver() {
  var item2 = document.querySelectorAll("ul li")[1];
  var event = new MouseEvent('mouseover', 
           {view: window, bubbles: true, cancelable: true});      
  var cancelled = !item2.dispatchEvent(event);
  if (cancelled) {
        // a handler called preventDefault.
        
  } else {
        // none of the handlers called preventDefault.
  }
}
You can find out more at
The question simulate a mouse click from 2011 or Trigger events in javascript from 2010 may be of use regarding the support in older browsers.