Biological filters create a space to grow more 'good' bacteria. The kind which loves to feed on Ammonia, and Nitrite, the potentially deadly chemicals which can cause great harm to your fish. You should add a suitable Bio Filter for your pond to ensure a safe environment for your fish.
Nitrate is also an issue for koi keepers as it is basically plant fertiliser, so can cause algae and blanket week issues, as well as other issues for your Koi...
For the Perfect Pond set up you should include Moving Bed Filtration and a Trickle Shower with BHM Media. This will help with all stages of theh Nitrogen Cycle and give better water conditions for your fish.
If on a tight budget a Mechanical Filter with a Shower with enough media for your pond would be our suggested approach.