In this study, we analyze state and metropolitan housing prices in the United States, focusing on the long range dependence of price volatility proxied by squared and absolute returns based on the fractional integration approach. We use quarterly data on state house price indices from each of the 50 U.S. states and the S&P/Case-Shiller house price indices for 20 U.S. metropolitan areas. Using parametric and semi-parametric long memory methods, we observe that most of the estimates of the fractional differencing parameter in the squared and absolute returns values are positive and constrained between 0 and 0.5, implying stationary long memory behavior.

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