Testing for Multiple Bubbles

67 Pages Posted: 9 Jan 2012  

Peter C. B. Phillips

Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics

Shuping Shi

Department of Economics, Macquarie University

Jun Yu

Singapore Management University; Singapore Management University - Lee Kong Chian School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: January 9, 2012

Abstract

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.

Keywords: Date-stamping strategy, Generalized sup ADF test, Multiple bubbles, Rational bubble, Periodically collapsing bubbles, Sup ADF test

JEL Classification: C15, C22

Suggested Citation

Phillips, Peter C. B. and Shi, Shuping and Yu, Jun, Testing for Multiple Bubbles (January 9, 2012). Cowles Foundation Discussion Paper No. 1843. Available at SSRN: https://ssrn.com/abstract=1981976 or http://dx.doi.org/10.2139/ssrn.1981976

Peter C. B. Phillips (Contact Author)

Yale University - Cowles Foundation ( email )

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University of Southampton

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Singapore Management University - School of Economics

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Shuping Shi

Department of Economics, Macquarie University ( email )

Australia

Jun Yu

Singapore Management University ( email )

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Singapore Management University - Lee Kong Chian School of Business ( email )

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