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From August 2009, the REINZ has been publishing a monthly Index that uses a different basis than their market median price.
The REINZ housing price index is put together using a technique known as stratification; basically it is an average of sale prices for common groups.
This Index was developed by the RBNZ, stratifying the REINZ data to give an average sale price for common groups. It therefore avoids the distortions that arise when there are sudden shifts in the type of houses being sold, especially in times of low volume.
Changes in the mix of properties sold each month can make it difficult to identify residential property price trends. A changing proportion of more (or less) expensive housing being actually sold in one month can move the median sale price even if the market prices for all properties have not changed.
For more on the stratification technique, see here.
The data is published here.
Unfortunately, this index is only available at this time for the broadest regions, and there is no facility to drill down any further.
August 2016: REINZ has stopped releasing most of this HPI data publicly. We will attempt to keep the series updated with data from other sources.