Data-sparse price indexes by spatio-temporal regularization and PCA An application to the Australian housing market

We present two novel approaches to overcome the limitations of data-sparse local house price indexes and combine them into a single model pipeline that is simple, computationally efficient, and interpretable. The first contribution is a new spatio-temporal regularization of least squares dummy variable models, such as the repeat sales regression used here. This regularization encodes prior knowledge of the proximity of houses in space and their sales in time. It handles missing values in a natural way. The second is nonlocal regularization using truncated principal component analysis (PCA) applied to the resulting national collection of local price indexes. The PCA loadings show that there are important underlying socioeconomic factors that can be leveraged in the construction of Australian market indexes. This PCA reveals important socioeconomic factors, showing that many local markets can be described by a few broad aspects of the national market, consisting of a general trend that contrasts regions influenced by the mining industry with Sydney and Melbourne, and another trend that highlights lifestyle.