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

Abstract

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. The Santa Anna MSA temporally causes house prices in six of the other seven MSAs, excluding only the San Luis Obispo MSA. The Oxnard MSA experiences the largest number of temporal effects from six of the seven MSAs, excluding only Los Angeles. The Santa Barbara MSA proves the most isolated. It temporally causes house prices in only two other MSAs (Los Angeles and Oxnard) and house prices in the Santa Anna MSA temporally cause prices in Santa Barbara. Third, we calculate out-of-sample forecasts in each MSA, using various vector autoregressive and vector error-correction 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 how theses time-series models can predict out-of-sample peaks and declines in house prices after in 2005 and 2006. Recursive forecasts, where we update the sample each quarter, provide reasonably good forecasts of the peaks and declines of the house price indexes.