Forecasting US real house price returns over 1831–2013: evidence from copula models

Abstract

Given the existence of nonnormality and nonlinearity in the data generating process of real house price returns over the period of 1831–2013, this article compares the ability of various univariate copula models, relative to standard benchmarks (naive and autoregressive models) in forecasting real US house price over the annual out-of-sample period of 1874–2013, based on an in-sample of 1831–1873. Overall, our results provide overwhelming evidence in favour of the copula models (Normal, Student’s t, Clayton, Frank, Gumbel, Joe and Ali-Mikhail-Huq) relative to linear benchmarks, and especially for the Student’s t-copula, which outperforms all other models both in terms of in-sample and out-of-sample predictability results. Our results highlight the importance of accounting for nonnormality and nonlinearity in the data generating process of real house price returns for the US economy for nearly two centuries of data.

Keywords:

• house price
• copula models
• forecasting

JEL Classification:

• C22
• C53
• R3

Acknowledgements

We would like to thank two anonymous referees for many helpful comments. However, any remaining errors are solely ours.

Notes

¹ For a detailed literature review on forecasting involving the US commercial and residential real estate markets, refer to Ghysels et al. (2013).

² Conventional wisdom argues that housing prices in the US rise more quickly and fully to market events that increase the equilibrium price than they do to market events that lower the equilibrium price. For example, the fall of housing prices during the recent financial crisis and Great Recession and beyond did not occur quickly enough to clear housing markets around the country, significantly slowing the recovery process. Recent studies (Genesove and Mayer, 2001; Engelhardt, 2001; Seslen, 2004; Kim and Bhattacharya, 2009; Balcilar et al., 2011, forthcoming) document evidence of such nonlinearity in housing prices. Several possible explanations for intrinsic nonlinearity in house prices exist. First, as noted above, households respond asymmetrically over the business cycle. Abelson et al. (2005) argue that households more likely buy when prices rise, because they expect further rises and try to avoid higher payments. Households will less likely buy or sell, however, due to loss aversion with falling house prices. Seslen (2004) argues that households exhibit forward-looking behaviour and a higher probability of trading up, during expansions, since equity constraints prove less binding. During the downswing of the housing market cycle, households less likely trade, implying downward rigidity of house prices. Loss aversion during the downswing more likely reduces the mobility of households as well as trading activity. Further, Muellbauer and Murphy (1997) note that the presence of lumpy transaction costs in the housing market can also cause nonlinearity. Given these issues, it makes sense to test for nonlinear housing price movements.

³ The best-fit student’s t-copula model had degrees of freedom equal to 20.

⁴ Based on the suggestions of an anonymous referee, we also conducted the Kolmogorov–Smirnov (KS) and the Cramér–von Mises (CvM) tests of misspecification. The KS test detected the Naïve, AR(1) and the AMH to be misspecified. The CvM test also found the same result as of the KS test, but interestingly, it could only reject the misspecification of the Gaussian (Normal) copula and the Student's t-copula at 1% level of significance. So overall, there is strong evidence (based on both tests) of misspecifcation for the Naïve and AR models, but not, in general, for the copula models. Further details of these results have been reported in Table A3 of the Appendix.