The Systematic Risk at the Crisis—A Multifractal Non-Uniform Wavelet Systematic Risk Estimation

Abstract

In the last decade, many factors, such as socio-political and econo-environmental ones, have led to a perturbation in the timeline of the worldwide development, and especially in countries and regions having political changes. This led us to introduce a new idea of risk estimation taking into account the non-uniform changes in markets by introducing a non-uniform wavelet analysis. We aim to explain the econo-political situation of Arab spring countries and the effect of the revolutions on the market beta. The main novelty is first the construction of a dynamic backward-forward model for missing data, and next the application of random non-uniform wavelets. The proposed procedure will be acted empirically on a sample corresponding to TUNINDEX stock as a representative index of the Tunisian market actively traded over the period from 14 January 2016 to 13 January 2021. The chosen 5-year period is important as it constitutes the first five years after the revolution and depends strongly on the socio-econo-political stability in the revolutionary countries. The results showed the efficiency of non-uniform wavelets in explaining the dynamics of the market well. They therefore may be good tools to explore important phenomena in the market such as the non-stationary aspect of financial series, non-constancy, and time-varying parameters. These facts in turn will have positive implications for investors as well as politicians in front of the evolution of the market. Besides, recommendations to extend the present method for other types of wavelets and markets will be of interest.

Wavelet Time-Scale Modeling of Brand Sales and Prices

“…We consider that more investigation into this volatile movement should be performed by improving tools such as the implementation of stochastic factors in the model and/or experimentation with non-uniform time-scale models, as in [13].…”

“…These characteristics of wavelet tools result in efficient algorithms in practice, outperforming classical techniques. Readers may refer, for instance, to [6][7][8][9][10][11][12][13][14].…”

A Wavelet Multiscale Mathematical Model for Quality of Life Index Measuring

“…known as the wavelet series or the wavelet decomposition of X(t), and it guarantees a complete reconstruction formula of the original series X(t) [12][13][14][15][16][17][18][19]33,34].…”

“…Wavelets indeed posses some special mathematical requirements useful in data representation. For example, for non-stationary data, wavelets are efficient descriptors for trend, volatility clustering, and variance due to their ability to take into account both frequency and time in the multi-resolution [12][13][14][15][16][17][18][19].…”

“…In our case, some values that are missing are unfortunately at the beginning of the period. We re-applied a modified version of the method developed in [17,33]. Our new idea consists first of applying a backward-forward method to reconstruct missing data.…”