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

By Peter C. B. Phillips, Shuping Shi, Jun Yu. 2015

1,139 citations recorded by the source corpus.

Recent work on econometric detection mechanisms has shown the effectiveness of recursive procedures in identifying and dating financial bubbles in real time. 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, this article 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 augmented Dickey–Fuller (ADF) test of Phillips et al. (“Explosive behavior in the 1990s NASDAQ: When did exuberance escalate asset values?” International Economic Review 52 (2011), 201–26; PWY) and delivers a consistent real‐time 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 collapses over this period, whereas the strategy of PWY and a related cumulative sum (CUSUM) dating procedure locate far fewer episodes in the same sample range.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/40f0f065d17297d84265d665d506b38a5ebf4fac

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Citations in the corpus

Testing for Bubbles in Cryptocurrencies with Time-Varying Volatility (2018, neutral): “Finally, we turn to the analysis of the time series of recursive DFr statistics to datestamp the bubbles, as in Phillips et al. (2011). They choose critical values that are close to the 4% level.”
Local explosion modelling by non‐causal process (2017, background): “…for bubbles would need to detect successive transitory explosions along the observed trajectory, and not an explosive behaviour on average, or a break point in the explosive behaviour on average, as in the approaches of Busetti and Taylor (2004), Phillips et al. (2011) or Phillips et al. (2015).”
Crypto-currency bubbles: an application of the Phillips–Shi–Yu (2013) methodology on Mt. Gox bitcoin prices (2015, methodology): “argued in Phillips et al. (2013a), the possibility that a bubble that bursts off in the sample period will render the variable pseudo-stationary if the period after the burst is also included in the ADF test.”
A systematic review of the bubble dynamics of cryptocurrency prices (2020, neutral): “Among the popular methodologies for detecting price bubbles could be found the Phillips et al. [2014] and Phillips et al. [2015] procedures.”
The economic value of Bitcoin: A portfolio analysis of currencies, gold, oil and stocks (2019, positive): “0084 This table presents the out-of-sample Sharpe ratio, variance and certainty equivalent at a daily rebalancing frequency for equal-weighted (EW ), global minimum-variance (GMV ) and short-sale constrained global minimum-variance strategies with historical (CGMV ) and DCC covariance forecasts (CGM”
Cryptocurrency trading: a comprehensive survey (2020, methodology): “[241, 242] (who applied a recursive augmented Dickey-Fuller algorithm, which is called PSY test) and Landsnes et al.”
Did Bubble Activity Intensify During COVID-19? (2020, methodology): “To circumvent the limitations of the ADF test, we also use the sup-ADF test which is rolling window based and its critical values are computed using Monte Carlo simulations; see Phillips et al. (2015) for details on the procedure and Table 1 for details on critical values.”
Bitcoin price and its marginal cost of production: support for a fundamental value (2018, positive): “Cheung, Roca, and Su (2015) as well as Su et al. (2018) use the Phillips, Shi, and Yu (2013, 2015)) method of bubble detection, confirming that multiple short-lived bubbles have characterized Bitcoin prices, with four ‘explosive bubbles’ since 2011 inclusive of the late-2017 period already…”