That is a good question and forms one of the most important parts of the assessment for this kind of application. Documentary evidence is required, official evidence according to the local law and especially evidence from official sources is required, i.e. independently verifiable evidence. Therefore if this is a problem you may not be able to meet the requirements of this category of application. However, every case is individual and would need to be assessed as such.
What kinds of source-of-funds documentation are required for New Zealand immigrant investors?
I wish to move to New Zealand and invest there, but I am worried about showing proof of my money from my country, which is largely cash-based and land is passed down through generations without much documentation. How can I still achieve my immigration goals?
New Zealand is very strict with source of funds. Generally you'll need evidence for the source of all funds to show every dollar has been legally earned or acquired. There is no time limit for this evidence and it's not unusual to require documentation that can be from many years ago as the full amount must be evidenced. It may still be possible to address these requirements in unusual situations where there are circumstances around cash with limited documentation, I recommend you discuss your situation with a licensed immigration adviser for New Zealand to understand what may be possible. Do note that Australia is generally less strict (under policy) with source of funds and that an Australian permanent residence visa will entitle you to residence in New Zealand - you may want to consider this as an alternative pathway if you can't apply directly to New Zealand.