Estimation of parameters of a multifractal process

• Autores: Fabrice Gamboa, Jean-Michel Loubes
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 16, Nº. 2, 2007, págs. 383-407
• Idioma: inglés
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• Resumen

  • Multifractal functions are widely used to model irregular signals such as turbulence, data stream or road traffic. Here, we consider multifractal functions defined as lacunar wavelet series observed in a white noise model. These random functions are statistically characterized by two parameters. The first parameter governs the intensity of the wavelet coefficients while the second one governs its sparsity. We construct estimators of these two parameters and discuss statistical properties of this important model: the rate of the Fisher information and a testing procedure to check the multifractal feature of an observed noisy signal.