Domain Authority is one of the major factors which affects the SERP’s outcome and is solely dependent on the power of the domain name. The measurement is based on the reputation of external/inbound links pointing back to the domain, as well as the age of the domain name and the popularity of the website.
Google acknowledges older domain names and not new ones as they already possessed credibility and popularity. Thus a domain name registered more than 10 years have more external links coming to its website then a recently registered domain name. Your probability of achieving higher domain authority will also be higher when the site consists more of inbound links than outbound.
The size for a website is based on the number of indexed pages you have. Generally, Google prefers websites with quality content and this will in turn result in more incoming links. That said, Domain Authority is a vital asset as it proves to be a financial viability to your website. Premium domain names that aged significantly usually have higher authority, and can be purchased through bids or at online marketplaces. Eventually, in order to achieve higher authority as well as SERP, you will need to have quality content and domain age influence.