Robustness and sensitivity of some wavelet multifractal models in fractal data modelling

Abstract

AbstractMany multifractal models such as self‐similar and scaling law types have been proved to be efficient modellers and estimators in many fields such as financial time series where the data hide fractal and multifractal structures, allowing its processing without sophisticated models to be difficult. However, in statistical analysis, a necessary part that should take place for any model and estimator consists in tests of performance such as confidence intervals and generally statistical tests to confirm the adequacy of the model. The present paper provides the consideration of multifractal models based on wavelets and self‐similar type processes to study statistical tests. To test the efficiency, accuracy and robustness of the models, different inferential statistics are introduced, provided with some empirical examples due to the EURO/USD exchange rate time series with a sample covering the period 03/01/2000 to 30/08/2022. Contrarily to existing works, we showed in the present work that quasi‐self‐similar type models are better for many reasons. They indeed guarantee the well fitting of the data dynamics, the nonlinearity in both the model and the multifractal spectrum, the renormalization parameters which may differ from one scale to another and the preservation of the quasi multiplicative structure.