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We consider the problem of neural network training in a time-varying context. Machine learning algorithms have excelled in problems that do not change over time. However, problems encountered in financial markets are often time-varying. We…
Using in a simple way the theory of non linear dynamical systems, we show that increasing climatic instabilities may be a qualitative warning sign for the occurrence of a nearby bifurcation, yielding a discontinuous and sudden climate…
Deep learning has shown impressive results in a variety of time series forecasting tasks, where modeling the conditional distribution of the future given the past is the essence. However, when this conditional distribution is…
Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In fact, they are…
In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…
We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…
Change-point detection methods are proposed for the case of temporary failures, or transient changes, when an unexpected disorder is ultimately followed by a readjustment and return to the initial state. A base distribution of the…
Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…
Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…
For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
The paper describes the deep learning approach for forecasting non-stationary time series with using time trend correction in a neural network model. Along with the layers for predicting sales values, the neural network model includes a…
Non-stationary time series with non-linear trends are frequently encountered in applications. We consider here the feasibility of accurately forecasting the signals of multiple such time series considering jointly when the number of…
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and…
We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
The modeling of risk situations that occur in a space-time framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial and temporal behaviour do not characterize the finite-dimensional…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be…