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

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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.

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Notes

  1. We exclude the El Centro MSA because the length of the time series on house prices proves too limited.

  2. Meen (1999) offers a similar discussion of UK for house price arbitrage between the Southeast to the Northwest, which he calls the “ripple effect.” He defines four explanations—migration, equity conversion, spatial arbitrage, and exogenous shocks with different timing of spatial effects.

  3. Stiglitz (1990) defines a bubble as follows. A high price exists because buyers anticipate that future prices will rise to even higher levels, not based on movements in fundamental factors.

  4. See LeSage (1999) and references cited therein for further details regarding the non-stationarity of most macroeconomic time series.

  5. See Dickey et al. (1991) and Johansen (1991, 1995) for further technical details.

  6. For an illustration, see Dua and Ray (1995).

  7. A longer version of this paper provides more details about the analysis and explicitly includes the weight matrices, F. See http://ideas.repec.org/p/nlv/wpaper/0912.html.

  8. See the longer version of this paper at http://ideas.repec.org/p/nlv/wpaper/0912.html for more details.

  9. Kuethe and Pede (2008) specify a similar prior, where they assume that the coefficient of the own-lagged term equals one and the sum of the lags of the other important variables, not including the own-lagged term, sums to one as well. Thus, their weighting scheme doubles the weight as compared to our scheme as well as requiring the own-lagged term to retain the coefficient of one, which reflects the essence of the random-walk averaging (RWA) prior.

  10. LeSage (1999) suggested ranges for the values for these hyperparameters.

  11. Note σ ijm in Eq. (8) is a generic term used to describe S k (i, j, m), k=1, 2, 3.

  12. Since the VEC specification constitutes the first differenced form of the three endogenous variables, and the optimal lag length used for the VAR is 6, we estimate all VEC models with 5 lags.

  13. The Santa Ana house price index just falls short of significantly causing house price index in San Luis Obispo at the 10-percent level.

  14. Here, we assume that Oxnard and San Luis Obispo share a portion of their border. In fact, they do not. But, we feel that they are close enough to justify the assumption.

  15. Note that the initial estimation period does not include the dramatic run up in home prices at the end of the out-of-sample forecast period.

  16. For this, we used the algorithm in the Econometric Toolbox of MATLAB, version R2006a.

  17. Note that if A t+n denotes the actual value of a specific variable in period t + n and t F t+n equals the forecast made in period t for t  +  n, the RMSE statistic equals the following: \( \sqrt {{\left[ {{{\sum\nolimits_1^N {\left( {{}_t{F_{t + n}} - {A_{t + n}}} \right)} }^2}/N} \right]}} \) where N equals the number of forecasts.

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Authors and Affiliations

  1. Department of Economics, University of Pretoria, Pretoria, 0002, South Africa

    Rangan Gupta

  2. College of Business, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV, 89154-6005, USA

    Stephen M. Miller

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  1. Rangan Gupta
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  2. Stephen M. Miller
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Correspondence to Stephen M. Miller.

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Gupta, R., Miller, S.M. The Time-Series Properties of House Prices: A Case Study of the Southern California Market. J Real Estate Finan Econ 44, 339–361 (2012). https://doi.org/10.1007/s11146-010-9234-7

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