Diagnosis and prediction of tipping points in financial markets: Crashes and rebounds

Abstract

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles. It embodies a positive feedback loop of higher return anticipations competing with negative feedback spirals of crash expectations. The power of the LPPL model is illustrated by two recent real-life predictions performed recently by our group: the peak of the Oil price bubble in early July 2008 and the burst of a bubble on the Shanghai stock market in early August 2009. We then present the concept of "negative bubbles", which are the mirror images of positive bubbles. We argue that similar positive feedbacks are at work to fuel these accelerated downward price spirals. We adapt the LPPL model to these negative bubbles and implement a pattern recognition method to predict the end times of the negative bubbles, which are characterized by rebounds (the mirror images of crashes associated with the standard positive bubbles). The out-of-sample tests quantified by error diagrams demonstrate the high significance of the prediction performance.

When organisations and ecosystems interact: toward a law of requisite fractality in firms

“…Consequently economies operate at or near the critical state. This shows up in the things like the price of cotton and many other economic realities described by Mandelbrot and Hudson (2004), consumer product sales (Moss, 2002;Sornette et al, 2004), entrepreneurial responses and results leading to different sized firms , and stock-market price volatilities (Zhou and Sornette, 2002, Sornette and Zhou, 2006, Jondeau et al, 2007Maskawa, 2007;Calvet and Fisher, 2008;Du and Ning, 2008;Eom et al, 2008;Kumar and Deo, 2009;Sornette and Woodard, 2009;Yan et al, 2010;McKelvey and Salmador Sanchez, 2011;Yalamova, 2011a, 2011b;Yalamova and McKelvey, 2011) -all of which show PL signatures. The parallel to sand avalanches is clear: from gravity to supply/demand; from irregular sand grains to irregular consumer and managerial decision processes and outcomes, from biological SOC to firms' and stock market SOC, the results are similar: PL shaped avalanches vs. PL shaped economic events and changes.…”

Prediction accuracy and sloppiness of log-periodic functions

“…Quite tellingly, early papers using LPPL to predict various kinds of crashes used only a single fit, which, of course, is problematic in the light of sloppiness. Recent papers try to build a probabilistic window for t c (Bastiaensen et al 2009, Jiang et al 2010, Yana et al 2010. The problem one faces is to estimate a probability distribution for t c from a single noisy time series.…”

“…However, when given a single run, predicting t c is much more difficult: the standard deviation on t c is about a half of t c À t. Hence, since the residuals are Gaussian distributed (we have checked that this is the case), the 20-80% confidence window, as chosen in recent papers on predictions with LPPL (Bastiaensen et al 2009, Jiang et al 2010, Yana et al 2010, corresponds to a width of about one standard deviation either side of the mean, hence ranges from (t þ t c )/2 to (3t c À t)/2, while the 5-95% confidence window (two standard deviations either side of the mean) ranges from t to 2t c À t. Therefore, when a crash warning is issued, the crash can occur any day at 95% confidence. Hence, predicting the date of a divergence is hard, even when the underlying time series is a real LPPL.…”

Adding Resilience to Financial Markets: Toward a Volatility-based, Power-Law Indicated, Resilience Initiation Point

“…But as Einstein once said: "Problems cannot be solved at the same level of awareness that created them." We thus propose a kind of Pascal's wager: Is it really a big risk for the community to explore the possibility of changing the (Yan, Woodard & Sornette, 2010) We develop resilience engineering applied against financial engineering by using the formation of a power-law (PL) distribution of stock market volatility dynamics as a tipping point. At this tipping point, we suggest that a set of stronger-to-weaker resilience devices may be applied.…”

“…We draw on basic Econophysics (West & Deering, 1995;Mantegna & Stanley, 2002;Vasconcelos, 2004), Hyman Minsky (1982Minsky ( , 1986, power-law science (Andriani & McKelvey, 2007, 2010a, the Hurst exponent (Struzik, 2001;Grech & Mazur, 2004;Cajueiro & Tabak, 2004;Alvarez-Ramirez et al, 2008;Masakawa, 2007;Yalamova, 2003Yalamova, , 2010), and logperiodic power laws (Yan, Woodard & Sornette, 2010) to identify the tipping point where efficient markets transform into crash-producing stock-market bubbles. This growing literature underlies our resilience-engineering approach for minimizing damage from inevitable extreme price volatilities and market crashes.…”