A propagating 1-dimensional wave revealed by unsupervised learning in a linear factor model.

Notes Residential property analysis for England and Wales 1995-2023. All tracked properties repriced to 2023, grouped by postcode district, computing aggregate \(£/m^2\). Repeat sales index computed on 3 partitions and displayed through time: (1) Top 0.27% and bottom 0.27% of districts (points q01 and q10) (2) NUTS2 regions’ districts split into quintiles on \(£/m^2\) (region lines) (3) 4 non-overlapping district price-bands are split on DES which is \(£/m^2\) relative to neighbouring districts (grey dashed iso-price lines). Linear factor model on subset of postcode areas defines factors, 40 time periods (-39:0) 1994:2023 of variable length to achieve equal factor 2,3 variance per period, betas for index sets 1-3 are by OLS. Periods 1:20 are forecast through VAR on factors, applying index betas for the index cycle forecasts. \(£/m^2\) (2023 prices) is the result, and horizontally theta is defined: \(\theta_\beta=tan^{-1}(\beta_3/\beta_2\)