This article proposes an alternative specification for the second stage of the Case-Shiller repeat-sales method. This specification is based on serial correlation in the deviations from the mean one-period returns on the underlying individual assets, whereas the original Case-Shiller method assumes that the deviations from mean returns by the underlying individual assets are i.i.d. The methodology proposed in this article is easy to implement and provides more accurate estimates of the standard errors of returns under serial correlation. The repeat-sales methodology is generally used to construct an index of prices or returns for unique, infrequently traded assets such as houses, art and musical instruments, which are likely to be prone to exhibit serial correlation in returns. We demonstrate our methodology on a data set of art prices and on a data set of real estate prices from the city of Amsterdam.
Graddy, K., Hamilton, J., & Pownall, R. A. J. (2012). Repeat sales indexes: Estimation without assuming that errors in asset returns are independently distributed. Real Estate Economics, 40(1), 131-166. https://doi.org/10.1111/j.1540-6229.2011.00307.x