How can I tell if a historical Case-Shiller home price index is based on FHFA data?
Examine the "source" field on the series.
When FHFA data is used, the individual series metadata indicates as much. For example, the documentation of series RXHCSHP1TIQ.MFLR will read: "Fiserv, Inc.; U.S. Federal Housing Finance Agency (FHFA)".
The source of the quarterly Case-Shiller Index, Fiserv, performs its own house price research whenever possible. However, certain geographic areas cannot or will not supply sales records. For such areas, Fiserv resorts to the methodologically-similar indexes published by FHFA, the Federal Housing Financing Agency (and before that, by OFHEO). Please see the background documentation in Mnemonic 411.
Every Data Buffet time series is annotated by several pieces of metadata. The textual "description" lists the purpose of the series and its measurement units. The "source" field describes the source (or sources) of the data; the name of the entity, and possibly the document and original identifier. If there are multiple sources, they are separated by semicolons.
The two textual metadata fields are visible in Mnemonic 411, View mode, and Basket output.
CoreLogic® Case-Shiller® Home Price Indexes