Well, one can use ockhams razor and plug the aggregate finance stats and household numbers in for each country: foreign investment will likely be related to the residual. That is, whatever amount is left over after domestic statistics and aggregate lending are taken into account. We don't have an accurate primary source for foreign investment, but we can reason.
The rba website would be my first stop in aus for aggregate finance stats available publicly. The Abs has some construction/hiding investment data, but there are some issues with definitions you'd need to take into account. And our neighbors across the pond, although I'm not a kiwi, I imagine will have very similar structures and data.
Additionally, such a simple model explains house prices quite well since the 1990s, across various markets with various levels of foreign investment, so we would need very good reasons to insert a "foreign investor" cause in there.
