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. This paper jointly analyses these three aspects of spatial data. A panel smooth transition regression model is applied 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. Evidence is found for heterogeneity in spatial spillovers of house prices across space and time: house prices in neighbouring regions spill over more in times of increasing neighbouring house prices then when neighbouring house prices are declining. 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.