Common Bubble Detection in Large Dimensional Financial Systems

Price bubbles in multiple assets are sometimes nearly coincident in occurrence. Such near-coincidence is strongly suggestive of co-movement in the associated asset prices and likely driven by certain factors that are latent in the financial or economic system with common effects across several markets. Can we detect the presence of such common factors at the early stages of their emergence? To answer this question, we build a factor model that includes I(1), mildly explosive, and stationary factors to capture normal, exuberant, and collapsing phases in such phenomena. The I(1) factor models the primary driving force of market fundamentals. The explosive and stationary factors model latent forces that underlie the formation and destruction of asset price bubbles, which typically exist only for subperiods of the sample. The paper provides an algorithm for testing the presence of and date-stamping the origination and termination of price bubbles determined by latent factors in a large-dimensional system embodying many markets. Asymptotics of the bubble test statistic are given under the null of no common bubbles and the alternative of a common bubble across these markets. We prove consistency of a factor bubble detection process for the origination and termination dates of the common bubble. Simulations show good finite sample performance of the testing algorithm in terms of its successful detection rates. Our methods are applied to real estate markets covering 89 major cities in China over the period January 2003 to March 2013. Results suggest the presence of three common bubble episodes in what are known as China's Tier 1 and Tier 2 cities over the sample period. There appears to be little evidence of a common bubble in Tier 3 cities.