^Agree, there is good info above!^
You are in the second phase of the cycle where you experience a large nitrite spike. Since for every 1 ppm of ammonia that is processed it turns into about 2.7 ppm of nitrite, that just goes to show it is going to take longer for your nitrifying bacteria to colonize enough to process all of the present nitrite. But trust me, your nitrite will go down!
As for the nitrates, they should not really be going down unless you have plants in your tank. Plants will use ammonia and nitrate as a source of nutrients. So, do you have plants in your tank?
Also, you always add ammonia in a fishless cycle at the 24 hour mark, regardless of when your ammonia goes to zero. Don't worry about loosing any autotrophic bacteria in that time period of no ammonia.
Our test kits, when they show zero for a certain value, are only so accurate. Even though our test kits show zero, there are still trace amounts of ammonia, in your case, present in the water that your bacteria are still using.
Also, there is one thing that 'may' speed up your cycle a bit, and that is a large (90%) water change! Sometime a large water change will help the bacteria colonize a little quicker right after the water change is performed. Remember, these bacteria live in the filter and not in the water column, so doing a water change is not going to take any of the bacteria out.
Helpful tips: A pH of 8.4 and a temp of 29C/84F is optimal for the growth of these bacteria!
-FHM