Related papers: Heavy-tails in economic data: fundamental assumpti…
We consider the task of heavy-tailed statistical estimation given streaming $p$-dimensional samples. This could also be viewed as stochastic optimization under heavy-tailed distributions, with an additional $O(p)$ space complexity…
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is…
Bayesian spatial modeling of heavy-tailed distributions has become increasingly popular in various areas of science in recent decades. We propose a Weibull regression model with spatial random effects for analyzing extreme economic loss.…
This article introduces a general class of heavy-tailed autoregressions for modeling integer-valued time series with outliers. The proposed specification is based on a heavy-tailed mixture of negative binomial distributions that features an…
In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the…
The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics,…
Financial markets provide an ideal frame for the study of crossing or first-passage time events of non-Gaussian correlated dynamics mainly because large data sets are available. Tick-by-tick data of six futures markets are herein considered…
This thesis evaluates most of the extreme mixture models and methods that have appended in the literature and implements them in the context of finance and insurance. The paper also reviews and studies extreme value theory, time series,…
We construct a two-tailed peak-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating…
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments.…
This paper addresses the statistical properties of time series driven by rational bubbles a la Blanchard and Watson (1982), corresponding to multiplicative maps, whose study has recently be revived recently in physics as a mechanism of…
This paper addresses the problem of estimating the tail index of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
Power grids are prone to failure. Time series of reliability measures such as total power loss or energy not supplied can give significant account of the underlying dynamical behavior of these systems, specially when the resulting…
Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability…
This paper proposes an empirical test of financial contagion in European equity markets during the tumultuous period of 2008-2011. Our analysis shows that traditional GARCH and Gaussian stochastic-volatility models are unable to explain two…
In this empirical paper we show that in the months following a crash there is a distinct connection between the fall of stock prices and the increase in the range of interest rates for a sample of bonds. This variable, which is often…
The study of loss function distributions is critical to characterize a model's behaviour on a given machine learning problem. For example, while the quality of a model is commonly determined by the average loss assessed on a testing set,…
In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…