When you're doing an insulation resistance test you have three types of current:
1) Capacitive current, as you put a charge on the conductor relative to its environment.
2) Polarizing current, as you orient the dipoles in the insulation in the present of a strong electric field.
3) Resistive current, that flows through imperfect insulation or tracks across contaminated surfaces.
Generally speaking the capacitive current goes away quickly as the capacitance charges to full voltage. When doing a 60 second DAR test, this is the function that is causing most of the rapid increase in resistance during the first part of the test. Once the capacitance is charged, the only current flowing is polarizing and resistive. You can see the effect of capacitive current by watching the needle on an analog megger when you turn it off: The needle often deflects the opposite direction as the capacitance discharges the current back through the metering circuit.
The polarizing current depends very largely on the type of insulation. Some insulation has a very rigid structure and does not polarize easily, and this means that running a 10 minute PI test will not yield "good" results, even though the insulation itself may be sound. Some old insulation will polarize excessively and you get very high PI readings, even though the insulation is very deteriorated. But when the resistance continues to slowly and steadily climb as the test progresses, you can be pretty sure that is because of polarization.
Finally you have resistive current. This very rapidly rises to a constant value. It's what tells you what is directly leaking through or over insulators, and is generally the largest component of the current flow, so also the biggest factor in your final resistance reading. When you hook up a megger and it reads a steady, unchanging value, that is because you have low capacitance, and low polarization, and the majority of your current is simply through leakage.