Whilst there are general guidelines on the criteria required for achieving each grade, ultimately, your grade is awarded at the discretion of your sensei.

Some senseis consider it disrespectful to ask if you can attend a grading - that you should leave such decisions to them. They prefer you to ask what you need to work on before you are ready for your next grade. This seems to me to be a pointlessly oblique approach, and I prefer my students to come straight out and ask. After all, they're paying me to teach them, and they have a right to find out how much progress they've made, compared to other students in the area.

You'll notice that kata and grading requirements are not listed beyond 2nd Dan. At that level, a rule of thumb is one year per dan grade between each grade and the next, thus from 2nd to 3rd dan, you'll wait three years, 3rd to 4th, four years, and so on.

Generally speaking, kata are not a primary requisite for grades much beyond 3rd dan, and beyond about 5th dan, grades are awarded for one's contribution to martial arts, rather than for martial ability.