Non-linear structures, chaos, and bubbles in U.S. regional housing markets

This study analyzes the nonlinear price pattern and its underlying source of nonlinearity for U.S. housing markets along with the plausible explanations of chaos and bubble-like characteristics during 1987 to 2019. The results from the BDS test show evidence of nonlinear dependence in overall U.S. housing markets along with home markets in twenty cities. The K-map Z-map analysis shows that nonlinear dependence in all cities is consistent with chaotic behavior. The nonlinear dependence is also substantiated with the use of Markov chain test where nonlinearity is due to the persistence of either positive or negative returns. Applying the duration dependence test on positive runs confirms that housing markets in all five regions experience some episodes of bubbles, except for home markets in Detroit and Minneapolis in Midwest region. A time reversibility test further provides supporting evidence that the mechanism generating nonlinear dependence in housing markets in all four cities in Midwest region comes from non-Gaussian innovations. Similar finding is reported in housing markets in other regions including Atlanta, Charlotte, Dallas, San Diego, and San Francisco, suggesting that a linear function with non-Gaussian error terms is appropriate for modelling these housing markets.