Related papers: Forecasting extreme events in collective dynamics:…
We propose a picture of stock market crashes as critical points in a hierachical system with discrete scaling. The critical exponent is then complex, leading to log-periodic fluctuations in stock market indexes. We present ``experimental''…
We apply two non-parametric methods to test further the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The analysis using the…
This paper is devoted to problem of detecting critical events at finiacial markets using methods of multifractal analysis. Namely, the local regularity of time-series is studied. As a result, one can find out a special behavior or signal of…
Motivated by the hypothesis that financial crashes are macroscopic examples of critical phenomena associated with a discrete scaling symmetry, we reconsider the evidence of log-periodic precursors to financial crashes and test the…
Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines. Here we present a novel approach, based on the Hilbert transform (HT). We show that temporal…
Several authors have noticed the signature of log-periodic oscillations prior to large stock market crashes [cond-mat/9509033, cond-mat/9510036, Vandewalle et al 1998]. Unfortunately good fits of the corresponding equation to stock market…
We propose that large stock market crashes are analogous to critical points studied in statistical physics with log-periodic correction to scaling. We extend our previous renormalization group model of stock market prices prior to and after…
The recently proposed discrete scale invariance and its associated log-periodicity are an elaboration of the concept of scale invariance in which the system is scale invariant only under powers of specific values of the magnification…
Forecasting volcanic eruptions remains a formidable challenge due to the inherent complexity and variability of volcanic processes. A key source of uncertainty arises from the sporadic nature of volcanic unrest, which is often characterised…
There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…
Detailed analysis of the log-periodic structures as precursors of the financial crashes is presented. The study is mainly based on the German Stock Index (DAX) variation over the 1998 period which includes both, a spectacular boom and a…
In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often…
The potential for complex systems to exhibit tipping points in which an equilibrium state undergoes a sudden and often irreversible shift is well established, but prediction of these events using standard forecast modeling techniques is…
We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not…
We argue that the word ``critical'' in the title is not purely literary. Based on our and other previous work on nonlinear complex dynamical systems, we summarize present evidence, on the Oct. 1929, Oct. 1987, Oct. 1987 Hong-Kong, Aug. 1998…
Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator which is realized…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…
Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points.…
The sporadic large fluctuations are seen in the stock market due to changes in fundamental parameters, technical setups, and external factors. These large fluctuations are termed as Extreme Events (EE). The EEs may be positive or negative…
Recent studies have shown that real-valued principal component analysis can be applied to earthquake fault systems for forecasting and prediction. In addition, theoretical analysis indicates that earthquake stresses may obey a wave-like…