There is a built-in component in Joomla, the Search component. It can gather the search expressions, what users typed on your frontend into the search box, and can make a statistics of it. Note that before the first use, you should enable to gather information on the options. Of course, if you are using the Universal Live Search, it will also collect these keywords for this component. But there is more power in our search module!
After you have some gathered keywords in this list, the search can recognize it, and offer these keywords for the user. But not in a usual way, it can complete the search expression for an existing one. And that's the point, it has many advantages:
You can set this option in the module manager by Show keyword suggestion parameter. See the image below:
Let's see it during operation:
When you start writing the expression, and if the suggestion appears you can press the right arrow key to complete your text.