# On the statistics of scaling exponents and the multiscaling value at risk

@article{Brandi2020OnTS, title={On the statistics of scaling exponents and the multiscaling value at risk}, author={Giuseppe Brandi and Tiziana di Matteo}, journal={arXiv: Risk Management}, year={2020} }

Scaling and multiscaling financial time series have been widely studied in the literature. The research on this topic is vast and still flourishing. One way to analyse the scaling properties of time series is through the estimation of scaling exponents. These exponents are recognized as being valuable measures to discriminate between random, persistent, and anti-persistent behaviours in time series. In the literature, several methods have been proposed to study the multiscaling property and in… Expand

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#### References

SHOWING 1-10 OF 65 REFERENCES

Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data.

- Medicine
- Physical review. E
- 2017

A measurement procedure which takes into account the presence of the filter function without the need of directly estimating it is devised and verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Expand

The use of scaling properties to detect relevant changes in financial time series: A new visual warning tool

- Mathematics, Economics
- 2021

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Measuring multiscaling in financial time-series

- Economics
- 2015

We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by… Expand

DETECTING MULTIFRACTAL PROPERTIES IN ASSET RETURNS: THE FAILURE OF THE "SCALING ESTIMATOR"

- Mathematics
- 2004

It has become popular recently to apply the multifractal formalism of statistical physics (scaling analysis of structure functions and f(α) singularity spectrum analysis) to financial data. The… Expand

On Hurst exponent estimation under heavy-tailed distributions

- Mathematics, Economics
- 2010

In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how… Expand

Log-Normal continuous cascades: aggregation properties and estimation. Application to financial time-series

- Mathematics, Economics
- 2008

Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied.… Expand

Log-normal continuous cascade model of asset returns: aggregation properties and estimation

- Economics
- 2013

Multifractal models and random cascades have been successfully used to model asset returns. In particular, the log-normal continuous cascade is a parsimonious model that has proven to reproduce most… Expand

Scaling behaviour in the dynamics of an economic index

- Mathematics
- Nature
- 1995

THE large-scale dynamical properties of some physical systems depend on the dynamical evolution of a large number of nonlinearly coupled subsystems. Examples include systems that exhibit… Expand

On Time-Scaling of Risk and the Square-Root-Of-Time Rule

- Mathematics, Economics
- 2003

Many financial applications, such as risk analysis and derivatives pricing, depend on time scaling of risk. A common method for this purpose, though only correct when returns are iid normal, is the… Expand

Multifractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method.

- Mathematics, Medicine
- Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1993

It is demonstrated that the method, based on the wavelet-transform modulus-maxima representation, works in most situations and is likely to be the ground of a unified multifractal description of self-affine distributions. Expand