The oldest martial arts systems had no ranking system of any sort. One simply had a belt and after some time, it was noticed that the senior practitioners had a much dirtier belt than the beginners, hence a black belt came to mean someone who had become proficient. Eventually a system for licensing and acknowledging ranks came into being, called the menkyo (license) system. Traditionally, one studied a style and received it completely then got a license to set up shop. This might require many years of work and one who has a license is customarily referred to as shihan or master teacher, in contrast to sensei or just plain teacher. Interestingly enough, sensei literally means "one who has gone before" rather than teacher.
In the late 1800's in Japan, the martial sport of judo was made by Jigoro Kano. Kano had studied older styles (notably kito ryu and tenjin shinyo ryu) and had become an excellent martial artist. He was the architect of the Japanese public school system. Most Japanese recognize his name in this capacity and are often surprised to hear that he did judo as well. As such, he decided that some martial art should be standard part of the curriculum and that a reward system should be put in place to encourage growth. It was he who, as near as can be told, implemented the first colored ranking system. The idea is to have 10 ranks, also called degrees leading up to a black belt (the so-called kyu ranks), then 10 ranks of black (the dan ranks). The ranks below black are obtainable in anywhere from 3 - 6 months each, while ranks of black normally take several years. A shihan in Kano's system is roughly a 5th degree black belt. The remaining ranks of black are awarded by committee for promoting the system, recognition for teaching etc. Kano's system has been very widely mimicked, and most martial arts have some ranking system. Degrees below black are pretty arbitrary and the colors vary greatly from one system to another.
For many years, hakko denshin ryu (HDR henceforth) followed a fairly traditional menkyo system. There are 4 ranks of black corresponding to the 4 sets of kata and then once the menkyo has been awarded, a purple belt is worn. Recently many decided that some form of ranking below black was needed, since it normally takes several years to obtain a black belt and students found this discouraging. This has been left up to the local instructors (so colors may vary from school to school) and only ranks of black are officially recognized by the national organization. In essence, instructors may encourage pupils with colored belt ranking, but these are viewed as meaningless. National conventions only recognize below and above black belt ranks, and every effort is made to work with practitioners at a level appropriate to them, rather than simply honoring their belt.
There are many issues with having colored belts and you should know the reason that HDR resisted adopting them for so long. The main reason is that they can be fairly quickly acquired, tempting many systems to simply give them out willy-nilly. There is no question that at as much as $50 an under-black rank, and several hundred dollars for a black belt, belt-testing is a major source of revenue for most instructors. One school I heard of was offering no less than 22 ranks below black at high prices for each one, plus it cost several thousand dollars to test for black. Another issue stemming from this is that having attained a rank is no guarantee of competence -- far too many schools require students to sign belt-testing contracts and students (quite rightly too) come to see this as vending belts. They've paid their money for a certain degree and are entitled to it. HDR insistence that no rank below black is really recognized is one attempt to stop this inflation.
On this account when dealing with practitioners of other styles, every effort should be made to ascertain what their level of experience is for the safety of everyone involved. Colors do not match between systems, abilities vary wildly and what might be standard at a rank in one system might not be present in another at all. Always err on the side of safety.