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This paper deals with tail diversification in financial time series through the concept of statistical independence by way of differential entropy and mutual information. By using moments as contrast functions to isolate the tails of the…
This book chapter illustrates how to apply extreme value statistics to financial time series data. Such data often exhibits strong serial dependence, which complicates assessment of tail risks. We discuss the two main approches to tail risk…
Fat tails in financial time series and increase of stocks cross-correlations in high volatility periods are puzzling facts that ask for new paradigms. Both points are of key importance in fundamental research as well as in Risk Management…
Large deviations for fat tailed distributions, i.e. those that decay slower than exponential, are not only relatively likely, but they also occur in a rather peculiar way where a finite fraction of the whole sample deviation is concentrated…
This article studies the financial time series data processing for machine learning. It introduces the most frequent scaling methods, then compares the resulting stationarity and preservation of useful information for trend forecasting. It…
We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…
Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena,…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a…
A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays $\tau$. The scale dependent behaviour of financial data can be divided into two regions.…
There is a large body of work, built on tools developed in mathematics and physics, demonstrating that financial market prices exhibit self-similarity at different scales. In this paper, we explore the use of analytical topology to…
The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index ($\alpha$), the Renyi exponents…
A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be…
Prices of commodities or assets produce what is called time-series. Different kinds of financial time-series have been recorded and studied for decades. Nowadays, all transactions on a financial market are recorded, leading to a huge amount…