An In-Sample and Out-of-Sample Empirical Investigation of the Nonlinearity in House Prices of South Africa

This paper first tests if housing prices in the five segments of the South African housing market, namely, large-middle, medium-middle, small-middle, luxury and affordable, exhibits non-linearity based on smooth transition autoregressive (STAR) models estimated using quarterly data covering the period of 1970:Q2 to 2009:Q3. We find overwhelming evidence of non-linearity in these five segments based on in-sample evaluation of the linear and non-linear models. We then provide further support for non-linearity by comparing one- to four-quarters-ahead out-of-sample forecasts of the non-linear time series model with those of the classical and Bayesian versions of the linear autoregressive (AR) models for each of these segments, over an out-of-sample horizon of 2001:Q1 to 2009:Q3, using an in-sample period from 1970:Q2 to 2000:Q4. Our results indicate that barring the one-, two and four-step(s)-ahead forecasts of the small-middle-segment, the non-linear model always outperforms the linear models.