Detecting criticality in complex univariate time-series: A case study of the US housing market crisis and other markets

The indices of asset markets are a key measure of an asset's value and how this varies over time. However, these indices are known to switch abruptly between qualitatively different behavioural epochs underscoring the complexity of collective decision-making in large, interacting populations of economic agents. A central question in the study of index dynamics is how to represent these transitions in a way that allows for both equilibrium and non-equilibrium behaviour in a dynamical systems framework. With this in mind, we sought to detect non-equilibrium transitions between stable equilibria in housing market data across thirteen OECD countries from 1975 through to 2019. We are able to precisely locate transitions using the quadrant scan method that has been used in earlier studies to detect critical points in other dynamical systems. We then use stochastic Catastrophe Theory to reconstruct the multi-modal distributions near the U.S. housing crisis point and show mode-switching behaviour of markets transitioning from one equilibrium to another. Our results are in contrast to other recent findings for the U.S. market that were unable to find a critical point near the 2007 crisis.