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Testing for Multiple Bubbles

Author

Listed:
  • Peter C.B. Phillips

    () (Yale University, University of Auckland, University of Southampton & Singapore Management University)

  • Shu-Ping Shi

    () (Research School of Economics, The Australian National University)

  • Jun Yu

    () (School of Economics, Singapore Management Unversity)

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.

Suggested Citation

  • Peter C.B. Phillips & Shu-Ping Shi & Jun Yu, 2011. "Testing for Multiple Bubbles," Working Papers 09-2011, Singapore Management University, School of Economics.
  • Handle: RePEc:siu:wpaper:09-2011
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    References listed on IDEAS

    as
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    Keywords

    Date-stamping strategy; Generalized sup ADF test; Multiple bubbles; Rational bubble; Periodically collapsing bubbles; Sup ADF test;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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