Related papers: Extreme Value Theory and the Solar Cycle
Extreme value theory for chaotic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by…
This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
Solar flares occur in complex sunspot groups, but it remains unclear how the probability of producing a flare of a given magnitude relates to the characteristics of the sunspot group. Here, we use Geostationary Operational Environmental…
We consider the extreme value theory of a hyperbolic toral automorphism $T: \mathbb{T}^2 \to \mathbb{T}^2$ showing that if a H\"older observation $\phi$ which is a function of a Euclidean-type distance to a non-periodic point $\zeta$ is…
The increasing occurrence of extreme weather events since the beginning of the 21st century has led to the development of new methods to attribute extreme events to anthropogenic climate change. The way in which the extreme event is defined…
The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in…
It is very important to forecast the future solar activity due to its effect on our planet and near space. Here, we employ the new version of the sunspot number index (version 2) to analyse the relationship between the solar maximum…
The Solar Cycle is reviewed. The 11-year cycle of solar activity is characterized by the rise and fall in the numbers and surface area of sunspots. A number of other solar activity indicators also vary in association with the sunspots…
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…
Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…
The purpose of this paper is to illustrate new techniques for computing multiday extreme precipitation taken from recent theoretical advancements in extreme value theory in the framework of dynamical systems, using historical precipitation…
Using neural networks as a prediction method, we attempt to demonstrate that forecasting of the Sun's sunspot time series can be extended to the spatial-temporal case. We employ this machine learning methodology to forecast not only in time…
Extreme events can come either from point processes, when the size or energy of the events is above a certain threshold, or from time series, when the intensity of a signal surpasses a threshold value. We are particularly concerned by the…
The prediction of extreme events in time series is a fundamental problem arising in many financial, scientific, engineering, and other applications. We begin by establishing a general Neyman-Pearson-type characterization of optimal extreme…
In this study, the cumulative effect of the empirical probability distribution of a random variable is identified as a factor that amplifies the occurrence of extreme events in datasets. To quantify this observation, a corresponding…
The present paper reviews results derived from statistical studies on solar activity indices. The prolonged minimum phase of cycle 23 raised the question of peculiarities inherent in cycle 23. The most important solar activity index is the…
The Schwabe (~11 yr) value for the annual sunspot number is sometimes uncritically applied to other measures of solar activity, direct and indirect, including the 10.7 cm radio flux, the inflow of galactic cosmic rays, solar flare…
The probability of occurrence of extreme solar particle events (SPEs) with the fluence of (>30 MeV) protons F30>10^{10} cm^{-2} is evaluated based on data of cosmogenic isotopes 14C and 10Be in terrestrial archives centennial-millennial…
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…