COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1843 Testing for Multiple Bubbles Peter C.B. Phillips, Shu-Ping Shi, and Jun Yu January 2012 Identifying and dating explosive bubbles when there is periodically
collapsing behavior over time has been a major concern in the economics literature and is
of great importance for practitioners. The complexity of the nonlinear structure inherent
in multiple bubble phenomena within the same sample period makes econometric analysis
particularly difficult. The present paper develops new recursive procedures for practical
implementation and surveillance strategies that may be employed by central banks and
fiscal regulators. We show how the testing procedure and dating algorithm of Phillips, Wu
and Yu (2011, PWY) are affected by multiple bubbles and may fail to be consistent. The
present paper proposes a generalized version of the sup ADF test of PWY to address this
difficulty, derives its asymptotic distribution, introduces a new date-stamping strategy
for the origination and termination of multiple bubbles, and proves consistency of this
dating procedure. Simulations show that the test significantly improves discriminatory
power and leads to distinct power gains when multiple bubbles occur. Empirical
applications are conducted to S&P 500 stock market data over a long historical period
from January 1871 to December 2010. The new approach identifies many key historical
episodes of exuberance and collapse over this period, whereas the strategy of PWY and the
CUSUM procedure locate far fewer episodes in the same sample range. |
