Abstract:
The aim of this paper is to present novel tests for the early causal diagnostic of positive
and negative bubbles in the S&P 500 index and the detection of End-of-Bubble signals
with their corresponding confidence levels. We use monthly S&P 500 data covering the
period from August 1791 to August 2014. This study is the first work in the literature
showing the possibility to develop reliable ex-ante diagnostics of the frequent regime
shifts over two centuries of data. We show that the DS LPPLS (log-periodic power law
singularity) approach successfully diagnoses positive and negative bubbles, constructs
efficient End-of-Bubble signals for all of the well-documented bubbles, and obtains for
the first time new statistical evidence of bubbles for some other events. We also compare
the DS LPPLS method to the exponential curve fitting and the generalized sup ADF test
approaches and find that DS LPPLS system is more accurate in identifying well-known
bubble events, with significantly smaller numbers of false negatives and false positives.
