Nonlinearities and tests of asset price bubbles

We find that incorporating nonlinearities into tests of asset price bubbles has important consequences for the results. We show this by comparing four tests using S&P 500 data. Our results indicate that the modification which incorporates nonlinear probabilities outperforms the other models in terms of select information criteria and a likelihood-based test. In addition, the coefficients associated with the nonlinear terms have the expected sign and the estimated probabilities display larger movements during the late 1910s, early 1930s/1940s, and the 2000s.