Extreme events: dynamics, statistics and prediction

Abstract

Abstract. We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts.

The Role of Oscillatory Modes in U.S. Business Cycles

“…On the other hand, the lower volatility during recessions in our analysis here is consistent with the predicted reduction in sensitivity to exogenous shocks, due to underutilized production capacity in the low phases of an EnBC. This so-called "vulnerability paradox" was also highlighted by Ghil et al (2011) and by Dumas et al (2013).…”

Extremes and Recurrence in Dynamical Systems

“…[63] -use of EVT. See also [5,4,64] comprehensive reviews. Another aspect to be mentioned is the role of noise or finite precision in observations.…”

“…We are most interested when the parameter λ lies in (3,4]. In that range of parameters there are maps f λ with a wide variety of behaviours.…”

“…Note that, as a consequence of the previous theorem, under the assumptions D(u n ) and D (u n ) the statement of Theorem 3.1.6 remains valid. Therefore, in a variety of applications where one needs to study extremes of time series featuring a sufficiently fast decay of correlations, GEV-and GPD-based statistical inference methods are used almost interchangeably, under the overall consensus that following the POT approach is more efficient when the time series are not exceptionally long [3,5,43,85,4,44]. Differences between the two methods emerge when extremes come in clusters; this is discussed below in Sections 3.2.2-3.4.…”

Preface "Extreme Events: Nonlinear Dynamics and Time Series Analysis"

“…A synthesis of the advances in the modeling, understanding and prediction of extreme events appears in the comprehensive review paper by Ghil et al (2011), which heads this special issue. Following this paper, 13 research papers deal with both methodological issues and applications.…”