Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series

Area of Science:

• Time Series Analysis
• Statistical Modeling
• Signal Processing

Background:

• The Hurst coefficient (H) quantifies self-similar decay in time-series autocorrelation.
• Fractional Brownian motion (fBm) signals are cumulative sums of fractional Gaussian noise (fGn).
• Accurate estimation of H is crucial for characterizing complex time-series data.

Purpose of the Study:

• To evaluate three-scaled windowed variance methods for estimating the Hurst coefficient (H).
• To compare the reliability of these methods against other established techniques.
• To determine data requirements for reliable H estimation.

Main Methods:

• Evaluation of standard, linear regression detrended, and bridge detrended scaled windowed variance methods.
• Estimation of H for fractional Brownian motion (fBm) signals.
• Analysis of bias and standard deviation of estimates for varying series lengths (N).

Main Results:

• Bias and standard deviation of estimates are <0.05 for N ≥ 2^9.
• Estimates are unreliable for short series (N < 2^8).
• Distinguishing H values differing by 0.1 requires N > 2^15 for 95% probability.
• Scaled windowed variance methods are more reliable than rescaled range, periodogram, and autocorrelation analyses, and comparable to dispersional analysis.

Conclusions:

• Three-scaled windowed variance methods provide reliable Hurst coefficient (H) estimation for fBm signals with adequate data.
• Sufficient data points (N ≥ 2^9) are essential for accurate and reliable H estimates.
• These methods offer advantages in applicability and reliability over several traditional time-series analysis techniques.