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

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.