Persistence in the return and volatility of home price indices

We examine the return and volatility of the Standard & Poor's/Case--Shiller (S&P/CS) real estate indices for evidence of long memory in the form of fractional differencing. Examining the long memory properties of these indices is relevant, in part, because effectively hedging real estate price risk through the construction of minimum variance dynamic hedge ratios requires proper modelling of long memory dynamics, and evidence of long memory would imply a violation of weak form efficiency. We find evidence of very persistent long memory in both the return and volatility of real estate indices. For real estate index returns, the evidence of persistent long memory contrasts sharply with other asset classes such as stocks, bonds and commodities. The evidence of long memory in real estate return volatility is in accordance with the volatility dynamics in other asset classes, although the degree of persistence is greater. We also find that some evidence of greater persistence may be due to nonlinearities in the underlying data generating process.