Testing for Multiple Bubbles 1: Historical Episodes of Exuberance and Collapse in the S&P 500

Published in International Economic Review, https://doi.org/10.1111/iere.12132</p

Testing for Multiple Bubbles 2: Limit Theory of Real Time Detectors

Singapore MOE Academic Research Tier 2Published in International Economic Review, https://doi.org/10.1111/iere.12131</p

Testing for Multiple Bubbles

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

Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior

Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. Empirical applications to the Nasdaq and to Australian and New Zealand housing data illustrate these specification issues and reveal their practical importance in testing.Unit root test, Mildly explosive process, Recursive regression, Size and power

Financial Bubble Implosion

Expansion and collapse are two key features of a financial asset bubble. Bubble expansion may be modeled using a mildly explosive process. Bubble implosion may take several different forms depending on the nature of the collapse and therefore requires some flexibility in modeling. This paper develops analytics and studies the performance characteristics of the real time bubble monitoring strategy proposed in Phillips, Shi and Yu (2014b,c, PSY) under alternative forms of bubble implosion that can be represented in terms of mildly integrated processes which capture various return paths to market normalcy. We propose a new reverse sample use of the PSY procedure for detecting crises and estimating the date of market recovery. Consistency of the dating estimators is established and the limit theory addresses new complications arising from the alternative forms of bubble implosion and the endogeneity effects present in the reverse regression. Simulations explore the finite sample performance of the strategy for dating market recovery and an illustration to the Nasdaq stock market is provided. A real-time version of the strategy is provided that is suited for practical implementation

Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500

Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles. These procedures are useful as warning alerts in surveillance strategies conducted by central banks and fiscal regulators with real time data. Use of these methods over long historical periods presents a more serious econometric challenge due to the complexity of the nonlinear structure and break mechanisms that are inherent in multiple bubble phenomena within the same sample period. To meet this challenge the present paper develops a new recursive flexible window method that is better suited for practical implementation with long historical time series. The method is a generalized version of the sup ADF test of Phillips, Wu and Yu (2011, PWY) and delivers a consistent date-stamping strategy for the origination and termination of multiple bubbles. Simulations show that the test significantly improves discriminatory power and leads to distinct power gains when multiple bubbles occur. An empirical application of the methodology is conducted on S&P 500 stock market data over a long historical period from January 1871 to December 2010. The new approach successfully identifies the well-known historical episodes of exuberance and collapse over this period, whereas the strategy of PWY and a related CUSUM dating procedure locate far fewer episodes in the same sample range

Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior

Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This paper aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of Phillips, Wu and Yu (2011), which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. Empirical applications to the Nasdaq and to Australian and New Zealand housing data illustrate these specification issues and reveal their practical importance in testing

Testing for Multiple Bubbles

Identifying and dating explosive bbles 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