How to setup a local wayback machine like that of Internet Archive?

I depend on our Government website for my research. There are some sites in those on which content and links appear and vanish on everyday basis. Their sites are terribly designed and they willfully take down some links or bury some things deep inside to make it hard for any one to find. The problem is I need to refer to something that was on the website months or years ago. Most of the time, I end up not finding it.

Is there a way to locally archive the sites and browse them like we do on wayback machine?