Yes, you can host your own domain but it will be much costlier than purchasing a hosting service. You will still have to purchase a domain name from a domain hosting service like GoDaddy, NameSilo, Dynadot, or others. Then you will need to have a strong business-level internet connection. There also has to be a server where you host your domain, so you will need to purchase and maintain a server, and the cost of that can be very high. You then need to choose an operating system and then a DNS server software. You will then have to configure the entire system.  In other words, it is going to be a very complicated process. Buying the best cheap website hosting service is a wiser choice.