Persistence, mean reversion and non-linearities in the US housing prices over 1830–2013

ABSTRACT

The objective of this study is to provide a direct estimate of the degree of persistence of measures of nominal and real house prices for the US economy, covering the longest possible annual sample of data, namely 1830–2013. The estimation of the degree of persistence accommodates for non-linear (deterministic) trends using Chebyshev polynomials in time. In general, the results show a high degree of persistence in the series along with a component of non-linear behaviour. In general, if we assume uncorrelated errors, non-linearities are observed in both nominal and real prices, but this hypothesis is rejected in favour of linear models for the log-transformation of the data. However, if autocorrelated errors are permitted, non-linearities are observed in all cases, and mean reversion is found in the case of logged prices, though given the wide confidence intervals, the unit root null hypothesis cannot be rejected in these cases.

KEYWORDS:

• US house prices
• long span annual data
• long memory
• non-linear trends

JEL CLASSIFICATION:

• C22
• R21
• R31

Acknowledgements

We would like to thank two anonymous referees for many helpful comments. The helpful comments of the editor and two reviewers are also much appreciated. However, any remaining errors are solely ours.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental Material

Supplemental data for this article can be accessed here.

Notes

¹ Further details regarding the dates of structural breaks for the nominal and real house price indices have been discussed in the data segment of the paper.

² Additional studies on this topic are that of Abraham and Hendershott (1996), Meese and Wallace (1994), Englund and Ioannides (1997), Malpezzi (1999), Meen (2002), Capozza et al. (2002, 2004), Gao, Lin, and Na (2009), Mikhed and Zemcik (2009), Beracha and Skiba (2011), Lean and Smyth (2013), André, Gil-Alana, and Gupta (2014), Gil-Alana, Barros, and Peypoch (2014), Gil-Alana, Barros, and Peypoch (2014) and Gupta and Majumdar (2015), among others.

³ An I(0) process is defined as a covariance stationary process with a spectral density function that is positive and finite at the long-run or zero frequency.

⁴ These conditions only include moments up to a second order.

⁵ See Cuestas and Gil-Alana (2015).

⁶ EViews and FORTRAN are used to conduct all the empirical analyses, and the codes are available upon request from the authors.

⁷ Further details of these tests are available upon request from the authors.

⁸ See Gil-Alana (2004) for further details.

Additional information

Funding

Luis A. Gil-Alana gratefully acknowledges the financial support from the Ministerio de Economía y Competitividad [ECO2014-55236]. Fernando Perez de Gracia also acknowledges the financial support from the Ministerio de Economía y Competitividad [ECO2014-55496].