Testing for Multiple Bubbles

Peter Phillips, Shuping Shi and Jun Yu

No 09-2011, Working Papers from Singapore Management University, School of Economics

Abstract: Identifying explosive bubbles that are characterized by periodically collapsing behavior over time has been a major concern in the literature and is of great importance for practitioners. The complexity of the nonlinear structure in multiple bubble phenomena diminishes the discriminatory power of existing tests, as evidenced in early simulations conducted by Evans (1991). Multiple collapsing bubble episodes within the same sample period make bubble diagnosis particularly di¢ cult and complicate attempts at econometric dating. The present paper systematically investigates these issues and develops new procedures for practical implementation and surveillance strategies by central banks. We show how the testing procedure and dating algorithm of Phillips, Wu and Yu (2011, PWY) is affected by multiple bubbles and may fail to be consistent. To assist performance in such contexts, the present paper proposes a generalized version of the sup ADF test of PWY that addresses the difficulty. The asymptotic distribution of the generalized test is provided and the test is shown to signfi cantly improve discriminatory power in simulations. The paper advances a new date-stamping strategy for the origination and termination of multiple bubbles that is based on this generalized test and consistency of the date-stamping algorithm is established. The new strategy leads to distinct power gains over the date-stamping strategy of PWY when multiple bubbles occur. Empirical applications are conducted with both tests along with their respective date-stamping technology to S&P 500 stock market data from January 1871 to December 2010. The new approach identi es many key historical episodes of exuberance and collapse over this period, whereas the strategy of PWY locates only two such episodes in the same sample range.

Keywords: Date-stamping strategy; Generalized sup ADF test; Multiple bubbles; Rational bubble; Periodically collapsing bubbles; Sup ADF test (search for similar items in EconPapers)
JEL-codes: C15 C22 (search for similar items in EconPapers)
Pages: 67 pages
Date: 2011-08
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (52)

Published in SMU Economics and Statistics Working Paper Series

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Related works:
Working Paper: Testing for Multiple Bubbles (2012)
Working Paper: Testing for Multiple Bubbles (2012)
Working Paper: Testing for Multiple Bubbles (2011)
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