A recursive regression methodology is used to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods provide a technology for identifying bubble behavior and consistent dating of their origination and collapse. Seven relevant financial series are investigated, including three financial assets (the Nasdaq index, home price index and asset-backed commercial paper), two commodities (the crude oil price and platinum

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 generalizedversionofthesupADFtestofPWYtoaddressthisdifficulty, 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

Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity —in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence.

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 righttailed 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.

This paper develops a double asymptotic limit theory for the persistent parameter () in an explosive continuous time model with a large number of time span (N) and a small number of sampling interval (h). The limit theory allows for the joint limits where N! 1 and h! 0 simultaneously, the sequential limits where N! 1 is followed by h! 0, and the sequential limits where h! 0 is followed by N! 1. All three asymptotic distributions are the same. The initial condition, either …xed or random, appears in the limiting distribution. The simultaneous double asymptotic theory is derived by using results recently obtained in Phillips and Magdalinos (2007) for the mildly explosive discrete time model and so a invariance principle applies. However, our asymptotic distribution is di¤erent from what was reported in Perron

Right-tailed unit root tests have proved promising for detecting exuberance in economic and …nancial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model speci…cation 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 di¤erent hypotheses and model speci…cations. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. An empirical application to Nasdaq data reveals the practical importance of model