Linear and nonlinear causality in financial markets.

Identifying and quantifying co-dependence between financial instruments is a key challenge for researchers and practitioners in the financial industry. Linear measures such as the Pearson correlation are still widely used today, although their limited explanatory power is well known. In this paper, we present a much more general framework for assessing co-dependencies by identifying linear and nonlinear causalities in the complex system of financial markets.

Efficient forecasting of chaotic systems with block-diagonal and binary reservoir computing.

The prediction of complex nonlinear dynamical systems with the help of machine learning has become increasingly popular in different areas of science. In particular, reservoir computers, also known as echo-state networks, turned out to be a very powerful approach, especially for the reproduction of nonlinear systems. The reservoir, the key component of this method, is usually constructed as a sparse, random network that serves as a memory for the system.

Identifying causality drivers and deriving governing equations of nonlinear complex systems.

Identifying and describing the dynamics of complex systems is a central challenge in various areas of science, such as physics, finance, or climatology. While machine learning algorithms are increasingly overtaking traditional approaches, their inner workings and, thus, the drivers of causality remain elusive. In this paper, we analyze the causal structure of chaotic systems using Fourier transform surrogates and three different inference techniques: While we confirm that Granger causality is exclusively able to detect linear causality, transfer entropy and convergent cross-mapping indicate that causality is determined to a significant extent by nonlinear properties.

Controlling nonlinear dynamical systems into arbitrary states using machine learning.

Controlling nonlinear dynamical systems is a central task in many different areas of science and engineering. Chaotic systems can be stabilized (or chaotified) with small perturbations, yet existing approaches either require knowledge about the underlying system equations or large data sets as they rely on phase space methods. In this work we propose a novel and fully data driven scheme relying on machine learning (ML), which generalizes control techniques of chaotic systems without requiring a mathematical model for its dynamics.

Reducing network size and improving prediction stability of reservoir computing.

Reservoir computing is a very promising approach for the prediction of complex nonlinear dynamical systems. Besides capturing the exact short-term trajectories of nonlinear systems, it has also proved to reproduce its characteristic long-term properties very accurately. However, predictions do not always work equivalently well.

Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing.

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the reproduction of the long-term properties of a nonlinear system. Yet, a thorough statistical analysis of the forecast results is missing.

Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization.

Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed to investigate the mutual dependencies of the stocks and their nature.