DNS servers. Is this possible?

I run a web server from home using a dns service (zonedit) because I don't have a static IP. When my ip address changes I update it with the dns service and the changes take place almost immediately.
My question is, if I set up a dns server on my own computer would I be able to associate an IP address from a hosted site.
For example: I would host with a site but use my own dns. That way, if I was to change hosting providers I could change the dns/ip information myself and not have the 3 days downtime because the dns would not actually change.

 

 

 

 

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