In this study we present a statistical analysis of the time series properties of the geographic regions in the OFHEO U.S. house price database. The time period for our study is first quarter 1975 through second quarter 2005. We perform an unobserved components, structural time series analysis of nine regional indexes and two super-regional factors and fit a classic “smooth trend plus cycle” model. We then apply bivariate unit root tests for absolute and relative convergence of the regions and factors, allowing for the possibility of a structural break. We find the two super-regions have slightly different patterns of trends and cycles until the early to mid-1990s, when a common pattern of strong and sustained price appreciation is seen. The evidence for regional convergence is mixed, with little for the first super-regional factor and some examples of relative convergence within the second factor. Thus support for a simple error correction model for regional house prices in our study is mixed.