Spatial heterogeneity and spatial dependence are two well established aspects of house price developments. However, the analysis of differences in spatial dependence across time and space has not gained much attention yet. In this paper we jointly analyze these three aspects of spatial data. We apply a panel smooth transition regression model that allows for heterogeneity across time and space in spatial house price spillovers and for heterogeneity in the effect of the fundamentals on house price dynamics. We find evidence for heterogeneity in spatial spillovers of house price developments across space and time: house price developments in neighboring regions spill over stronger in times of increasing neighboring house prices compared to declining neighboring house prices. This is interpreted as evidence for the disposition effect. Moreover, heterogeneity in the effect of the fundamentals on house price dynamics could not be detected for all variables; real per capita disposable income and the unemployment rate have a homogeneous effect across time and space.