The Time-Series Properties of House Prices: A Case Study of the Southern California Market

We examine the time-series relationship between house prices in eight Southern California metropolitan statistical areas (MSAs). First, we perform cointegration tests of the house price indexes for the MSAs, finding seven cointegrating vectors. Thus, the evidence suggests that one common trend links the house prices in these eight MSAs, a purchasing power parity finding for the house prices in Southern California. Second, we perform temporal Granger causality tests revealing intertwined temporal relationships. The Santa Anna MSA leads the pack in temporally causing house prices in six of the other seven MSAs, excluding only the San Luis Obispo MSA. The Oxnard MSA experienced the largest number of temporal effects from other MSAs, six of the seven, excluding only Los Angeles. The Santa Barbara MSA proved the most isolated in that it temporally caused house prices in only two other MSAs (Los Angeles and Oxnard) and house prices in the Santa Anna MSA temporally caused prices in Santa Barbara. Third, we calculate out-of-sample forecasts in each MSA, using various vector autoregressive (VAR) and vector error-correction (VEC) models, as well as Bayesian, spatial, and causality versions of these models with various priors. Different specifications provide superior forecasts in the different MSAs. Finally, we consider the ability of theses time-series models to provide accurate out-of-sample predictions of the decline in the house prices after their peaks in 2005 and 2006. Recursive forecasts, where the sample is updated each quarter, provide reasonably good forecasts of timing of the peak and decline if the house prices.