I apologize. I left out some time spans.
From White to 1st Black for a new student in ATA should take about three years. Another year and a half for 2nd Degree. After that, you are not eligible to test for the number of years in your rank, so a 2nd Degree would have to wait a minimum of two years before testing. And of course, there is always the possibility of no-changing on the test, so it might take longer to achieve the next rank. So for a rock star who seriously busts their hump training, we're looking at 6 1/2 - 7 years for 3rd Degree.
Someone with prior training already knows the lion's share of the techniques. As I said earlier, that will cut down on time as they come up through the ranks. So a 3rd Degree in ITF, I think, should be able to get to 3rd Degree in ATA in about 3 years or so. That's just a SWAG on my part.