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Related Concept Videos

Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Evaluating maximum likelihood estimation methods to determine the Hurst coeficient.

C M Kendziorski1, J B Bassingthwaighte, P J Tonellato

  • 1Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI 53233, USA.

Physica A
|August 21, 2012
PubMed
Summary
This summary is machine-generated.

A new method reliably estimates the Hurst coefficient (H) for long memory time series, correcting biases found in the original S-MLE approach for fractional Gaussian noise and differenced processes.

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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.