A Comparative Study of the Performance of Estimating Long-Memory Parameter Using Wavelet-Based Entropies

In this paper, we discuss the performance of four estimators in the wavelet domain in order to estimate the parameter of stationary long-memory models. The goal of our article is to construct a wavelet estimate for the fractional differencing parameter d where the selection of the optimal level of the multiresolution decomposition is given by three entropies-based approaches, as alternative to subjective determination of the multiscale wavelet decomposition methodology. We have shown by Monte Carlo experiments that the concentration in an $$l^{p}$$ l p norm entropy-based procedure improves considerably the other suggested entropy-based determination of the optimal decomposition level considered. The simulation results also show that the concentration in an $$l^{p}$$ l p norm entropy-related criterion and the maximum scale decomposition method performs better in most cases and provides evidence of the power of the wavelet methods. We then applied wavelet-entropy estimators to some daily stock market indices.