Evaluating maximum likelihood estimation methods to determine the Hurst coeficient

Area of Science:

• Time Series Analysis
• Statistical Modeling

Background:

• The Hurst coefficient (H) quantifies long memory in time series, crucial for understanding processes like fractional differencing (fd) and fractional Gaussian noise (fGn).
• Distinguishing between fd and fGn processes is challenging in practice.
• Accurate estimation of H is vital for characterizing time series behavior.

Purpose of the Study:

• To evaluate the performance of the maximum likelihood estimation (S-MLE) method for estimating the Hurst coefficient (H).
• To assess S-MLE's accuracy for both fractionally differenced (fd) and fractional Gaussian noise (fGn) processes.
• To develop a modified method for unbiased H estimation.

Main Methods:

• Evaluation of the S-MLE method implemented in S-PLUS.
• Testing S-MLE on synthetic fd and fGn processes of varying lengths.
• Development and testing of a modified bias-correction method.

Main Results:

• The S-MLE method produced biased Hurst coefficient (H) estimates for fGn processes and short fd processes (length < 2^10).
• The modified method demonstrated reliable H estimates for both fd and fGn processes.
• The modified method achieved unbiased results for series lengths >= 2^11.

Conclusions:

• The original S-MLE method exhibits significant bias in estimating the Hurst coefficient (H) for certain time series types and lengths.
• A modified estimation approach effectively corrects for bias, providing accurate H values.
• The improved method enhances the analysis of long memory time series, particularly for distinguishing between fd and fGn processes.