Hurst Parameter Estimation Methods: Comparative Study and Application
Hurst Parameter Estimation Methods: Comparative Study and Application
Author(s): Imane El Wahli, Radouane El Khchine, Zine Elabidine Guennoun, Youness LaaroussiSubject(s): Economy, Business Economy / Management, Accounting - Business Administration
Published by: Reprograph
Keywords: exchange rate; fractional Brownian motion; Hurst exponent; Hurst parameter estimators; mean square error;
Summary/Abstract: Given the importance of Hurst exponent (H), the key parameter of fractional Brownian motion, several methods are developed to estimate it more efficiently. In this paper, we propose a comparative analysis of five estimation methods for H, namely the Standardized Range (R/S) method, the Detrended Moving Average algorithm (DMA), Generalized Quadratic Variation (GQV) Estimator, the log-Periodogram and the method based on the wavelet analysis. To realize this objective, independently of characteristics of the series, we proceed by simulation of several signals test of different sizes and of a known H values. For each method, we evaluate the estimator quality by measuring their bias and variance i.e. the mean square error. The most efficient method will be used to analyse an important economic series, relating to the behaviour ofMoroccan exchange rate series vis-à-vis the Dollar and the Euro from December, 2000 to December, 2017.
Journal: Journal of Applied Economic Sciences (JAES)
- Issue Year: XIII/2018
- Issue No: 56
- Page Range: 326-336
- Page Count: 11
- Language: English
