Related papers: Recurrence Plot and Recurrence Quantification Anal…
We explore the evolution of daily returns of four major US stock market indices during the technology crash of 2000, and the financial crisis of 2007-2009. Our methodology is based on topological data analysis (TDA). We use persistence…
We propose two rational expectation models of transient financial bubbles with heterogeneous arbitrageurs and positive feedbacks leading to self-reinforcing transient stochastic faster-than-exponential price dynamics. As a result of the…
We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot based analysis for…
We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series. Our argument is based on the Log-Periodic Power Law Singularity (LPPLS)…
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…
The financial markets are understood as complex dynamical systems whose dynamics is analysed mostly using nonstationary and brief data sets that usually come from stock markets. For such data sets, a reliable method of analysis is based on…
This paper considers the problem of nonstationary process monitoring under frequently varying operating conditions. Traditional approaches generally misidentify the normal dynamic deviations as faults and thus lead to high false alarms.…
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient {\rho} as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence…
Cross-correlation analysis is a powerful tool for understanding the mutual dynamics of time series. This study introduces a new method for predicting the future state of synchronization of the dynamics of two financial time series. To this…
The knowledge of transitions between regular, laminar or chaotic behavior is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there…
The growing study of time series, especially those related to nonlinear systems, has challenged the methodologies to characterize and classify dynamical structures of a signal. Here we conceive a new diagnostic tool for time series based on…
PyRQA is a software package that efficiently conducts recurrence quantification analysis (RQA) on time series consisting of more than one million data points. RQA is a method from non-linear time series analysis that quantifies the…
Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic…
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis (RQA) and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state…
Used to investigate the presence of distinctive recurrent behaviours in natural processes, the recurrence plots can be applied to the analysis of economic data, and, in particular, to the characterization of exchange rates of currencies…
A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intradaily structures in the…
We propose an algorithm for the detection of recurrence domains of complex dynamical systems from time series. Our approach exploits the characteristic checkerboard texture of recurrence domains exhibited in recurrence plots (RP). In phase…
Probability Quantification (PQ) predictions of the efficacy of safety-critical protective systems is challenging. Yet, the popularity of PQ methodologies (e.g., Probabilistic Risk Assessment (PRA), Quantitative Risk Analysis (QRA) and…
Our research presents a new approach for forecasting the synchronization of stock prices using machine learning and non-linear time-series analysis. To capture the complex non-linear relationships between stock prices, we utilize recurrence…
Trajectories of units moving on networks are relevant for nonlinear dynamical systems as diverse as polymers, ocean drifters, and human mobility. Although RQA is a well-researched tool with applications in many areas, it has rarely been…