Tracking performance and robustness analysis of Hurst estimators for multifractional processes

In this study, the authors focus on the tracking performance and the robustness of 12 sliding-windowed Hurst estimators for multifractional processes with linear trend local Hölder exponent, noisy multifractional processes and multifractional processes with infinite second-order statistics. Four types of multifractional processes are synthesised to test the tracking performance and robustness of these 12 sliding-windowed Hurst estimators. They are (i) noise-free multifractional process; (ii) multifractional process corrupted by 30-dB signal-to-noise ratio (SNR) white Gaussian noise; (iii) multifractional process corrupted by 30-dB SNR impulse noise; and (iv) multifractional stable process, which has no finite second-order statistics. Furthermore, the standard error of different sliding-windowed Hurst estimators are calculated in order to quantify the accuracy and robustness. This study provides a guideline and principle in the selection of Hurst estimators for noise-free multifractional process, noise-corrupted multifractional process and multifractional process with infinite second-order statistics. The results of this analysis show that the sliding-windowed Kettani and Gubner̈s method provides the best-tracking performance for multifractional processes with linear trend local Hölder exponent and good robustness to noise.