Magnificent 7: unsustainable growth and systemic risk

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 logperiodic 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. We use the LPPL model in one of its incarnations to analyze two bubbles and subsequent market crashes in two important indexes in the Chinese stock markets between May 2005 and July 2009. Both the Shanghai Stock Exchange Composite index (US ticker symbol SSEC) and Shenzhen Stock Exchange Component index (SZSC) exhibited such behavior in two distinct time periods: 1) from mid-2005, bursting in October 2007 and 2) from November 2008, bursting in the beginning of August 2009. We successfully predicted time windows for both crashes in advance [24, 1] with the same methods used to successfully predict the peak in mid-2006 of the US housing bubble [37] and the peak in July 2008 of the global oil bubble [26]. The more recent bubble in the Chinese indexes was detected and its end or change of regime was predicted independently by two groups with similar results, showing that the model has been well-documented and can be replicated by industrial practitioners. Here we present more detailed analysis of the individual Chinese index predictions and of the methods used to make and test them. We complement the detection of log-periodic behavior with Lomb spectral analysis of detrended residuals and (H, q)-derivative of logarithmic indexes for both bubbles. We perform unit-root tests on the residuals from the log-periodic power law model to confirm the Ornstein-Uhlenbeck property of bounded residuals, in agreement with the consistent model of ‘explosive’ financial bubbles [16].

Name change for UltraStrip

Bubble diagnosis and prediction of the 2005–2007 and 2008–2009 Chinese stock market bubbles

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

Testing for financial crashes using the Log Periodic Power Law model

Market regime detection via realized covariances

Deep Gaussian processes (DGPs) are increasingly popular as predictive models in machine learning for their nonstationary flexibility and ability to cope with abrupt regime changes in training data. Here, we explore DGPs as surrogates for computer simulation experiments whose response surfaces exhibit similar characteristics. In particular, we transport a DGP’s automatic warping of the input space and full uncertainty quantification, via a novel elliptical slice sampling Bayesian posterior inferential scheme, through to active learning strategies that distribute runs nonuniformly in the input space—something an ordinary (stationary) GP could not do. Building up the design sequentially in this way allows smaller training sets, limiting both expensive evaluation of the simulator code and mitigating cubic costs of DGP inference. When training data sizes are kept small through careful acquisition, and with parsimonious layout of latent layers, the framework can be both effective and computationally tractable. Our methods are illustrated on simulation data and two real computer experiments of varying input dimensionality. We provide an open source implementation in the deepgp package on CRAN.

Geomagnetic indices can be divided in two families, sometimes called “mean” and “range” families, which reflect different interactions between solar and terrestrial processes on time scales ranging from hourly to secular and longer. We are interested here in trying to evaluate secular change in the correlations between these indices and variations in solar activity as indicators of secular changes in solar behavior. We use on one hand daily values of geomagnetic indices Dst and ζ (members of the “mean” family), and Ap and aa (members of the “range” family), and on the other hand solar indices WN (sunspot number), F10.7 (radio flux), interplanetary magnetic field B and solar wind speed v over the period 1955–2005. We calculate correlations between pairs of geomagnetic indices, between pairs of solar indices (including the composite Bv2), and between pairs consisting in a geomagnetic vs a solar index, all averaged over one to eleven years. The relationship between geomagnetic indices depends on the evolution of solar activity; strong losses of correlation occur during the declining phase of solar cycle 20 and in solar cycle 23. We confirm the strong correlation between aa and Bv2 and to a lesser extent between Dst and B. On the other hand, correlations between aa or Dst and v are non‐stationary and display strong increases between 1975 and 2000. Some geomagnetic indices can be used as proxies for the behavior of solar wind indices for times when these were not available. We discuss possible physical origins of sub‐decadal to secular evolutions of correlations and their relation with the character of solar activity (correlation of DP2 substorms and main storm occurrence, generation of toroidal field of a new cycle during descending phase of old cycle and prediction of next cycle, and also links with coupling of nonlinear oscillators and abrupt regime changes).

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 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. We use the LPPL model in one of its incarnations to analyze two bubbles and subsequent market crashes in two important indexes in the Chinese stock markets between May 2005 and July 2009. Both the Shanghai Stock Exchange Composite and Shenzhen Stock Exchange Component indexes exhibited such behavior in two distinct time periods: 1) from mid-2005, bursting in Oct. 2007 and 2) from Nov. 2008, bursting in the beginning of Aug. 2009. We successfully predicted time windows for both crashes in advance with the same methods used to successfully predict the peak in mid-2006 of the US housing bubble and the peak in July 2008 of the global oil bubble. The more recent bubble in the Chinese indexes was detected and its end or change of regime was predicted independently by two groups with similar results, showing that the model has been well-documented and can be replicated by industrial practitioners. Here we present more detailed analysis of the individual Chinese index predictions and of the methods used to make and test them.

Interpreting the movement of oil prices: Driven by fundamentals or bubbles?

The talent training evaluation model not only helps to evaluate the talent itself but also provides feedback on the content of the talent training evaluation. Therefore, this paper establishes an efficient and intelligent talent training evaluation model for accounting professionals based on the logarithmic cycle power law model. The main content of talent training evaluation is set as general knowledge skills, professional thinking, and values. The log-periodic power-law model and the least squares method are combined to reduce the dimensionality of the nonlinear parameters of the judging content and to quantify the judging of intelligent accounting professional talent training in universities, which is convenient for the calculation of linear functions. With the help of log-periodic power-law oscillation to prove that talent training is changing in a cyclical pattern, the feasibility of its prediction is demonstrated. The study shows that the talent cultivation judgment model constructed based on the log-periodic power-law model is very accurate, especially in talent cultivation value judgment prediction. The model achieves zero error in the prediction of some data, and the maximum error between prediction and actual is only 6%. In the judgment of general knowledge and skill cultivation, the maximum error between the prediction and the actual score of the model is no more than 2 points. This shows that the talent development evaluation model based on the log-periodic power law model can make accurate predictions of talent development evaluation.

The global economy frequently experiences cycles of rapid growth followed by abrupt crashes, challenging economists and analysts in forecasting and risk management. Crashes like the dot-com bubble crash and the 2008 global financial crisis caused huge disruptions to the world economy. These crashes have been found to display somewhat similar characteristics, like rapid price inflation and speculation, followed by collapse. In search of these underlying patterns, the Log-Periodic Power-Law (LPPL) model has emerged as a promising framework, capable of capturing self-reinforcing dynamics and log-periodic oscillations. However, while log-periodic structures have been tested in developed and stable markets, they lack validation in volatile and developing markets. This study investigates the applicability of the LPPL framework for modeling financial crashes in the Brazilian stock market, which serves as a representative case of a volatile market, particularly through the Bovespa Index (IBOVESPA). In this study, daily data spanning 1993 to 2025 is analyzed to model pre-crash oscillations and speculative bubbles for five major market crashes. In addition to the traditional LPPL model, autoregressive residual analysis is incorporated to account for market noise and improve predictive accuracy. The results demonstrate that the enhanced LPPL model effectively captures pre-crash oscillations and critical transitions, with low error metrics. Eigenstructure analysis of the Hessian matrices highlights stiff and sloppy parameters, emphasizing the pivotal role of critical time and frequency parameters. Overall, these findings validate LPPL-based nonlinear modeling as an effective approach for anticipating speculative bubbles and crash dynamics in complex financial systems.

Purpose The occurrence and unpredictability of speculative bubbles on financial markets, and their accompanying crashes, have confounded economists and economic historians worldwide. The purpose of this paper is to diagnose and detect the bursting of shipping bubbles ex ante, and to qualify the patterns of shipping price dynamics and the bubble mechanics, so that appropriate counter measures can be taken in advance to reduce side effects arising from bubbles. Design/methodology/approach Log periodic power law (LPPL) model, developed in the past decade, is used to detect large market falls or “crashes” through modeling of the shipping price dynamics on a selection of three historical shipping bubbles over the period of 1985 to 2016. The method is based on a nonlinear least squares estimation that yields predictions of the most probable time of the regime switching. Findings It could be concluded that predictions by the LPPL model are quite dependent on the time at which they are conducted. Interestingly, the LPPL model could have predicted the substantial fall in the Baltic Dry Index during the recent global downturn, but not all crashes in the past. It is also found that the key ingredient that sets off an unsustainable growth process for shipping prices is the positive feedback. When the positive feedback starts, the burst of bubbles in shipping would be influenced by both endogenous and exogenous factors, which are crucial for the advanced warning of the market conversion. Originality/value The LPPL model has been first applied into the dry bulk shipping market to test a couple of shipping bubbles. The authors not only assess the predictability and robustness of the LPPL model but also expand the understanding of the model and explain patterns of shipping price dynamics and bubble mechanics.

Regime shifts caused by adaptive dynamics in prey–predator models and their relationship with intraspecific competition

Retrospective analysis and forecasting of streamflows using a shifting level model