Related papers: Inferring long memory using extreme events
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
Weather extremes produce major impacts on society and ecosystems and are likely to change in likelihood and magnitude with climate change. However, very low probability events are hard to characterize statistically using observations or…
Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
An increasing body of research focuses on using neural networks to model time series. A common assumption in training neural networks via maximum likelihood estimation on time series is that the errors across time steps are uncorrelated.…
We discuss the frequency of desynchronization events in power grids for realistic data input. We focus on the role of time correlations in the fluctuating power production and propose a new method for implementing colored noise that…
The occurrence of extreme events like heavy precipitation or storms at a certain location often shows a clustering behaviour and is thus not described well by a Poisson process. We construct a general model for the inter-exceedance times in…
To make informed decisions in natural environments that change over time, humans must update their beliefs as new observations are gathered. Studies exploring human inference as a dynamical process that unfolds in time have focused on…
We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class of processes includes, among others, ARMA processes with regularly…
Out-of-equilibrium disordered systems may form memories of external driving in a remarkable fashion. The system "remembers" multiple values from a series of training inputs yet "forgets" nearly all of them at long times despite the inputs…
It is demonstrated how to generate time series with tailored nonlinearities by inducing well- defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with…
We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The long memory makes clusters larger, and the asymptotic behaviour of the size of the…
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
Many time series in natural and social sciences can be seen as resulting from an interplay between exogenous influences and an endogenous organization. We use a simple (ETAS) model of events occurring sequentially, in which future events…
Trend change prediction in complex systems with a large number of noisy time series is a problem with many applications for real-world phenomena, with stock markets as a notoriously difficult to predict example of such systems. We approach…
Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations in order to…
The role of memory time fluctuations for instabilities in random media is considered. It is shown that fluctuations can result in infinitely fast growth of statistical moments. The effect is demonstrated in the framework of light…