Depending on the structure itself you need to think about uplift and may want more than a just a precast base sitting on the ground
This. Picture a trampoline, which really doesn't have much to catch the wind (nothing but a big screen) and how they just sail away.
If the pergola doesn't have any sort of fabric, the wind may not get it, but if there's any exposure to the breeze, the wind will find a way.
As others have said, the rule in ND USED TO BE, if it's attached to your house or garage, it will need to have footings that go down past frost (48").
Say the posts are 4x4's. If you dig a hole 50" deep, place pea gravel in the bottom of the hole for drainage, drop a concrete block down for the 4x4 to rest upon, and then scab on a 12" long piece of 2x4 on all four sides, at the bottom (this keeps the 4x4 from pulling out of the ground) you should be all set.