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A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry.

S Lu1, K H Ju, K H Chon

  • 1Department of Electrical Engineering and Center for Biomedical Engineering, City College of the City University of New York, NY 10031, USA.

IEEE Transactions on Bio-Medical Engineering
|October 5, 2001
PubMed
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A novel affine geometry-based algorithm accurately identifies linear and nonlinear autoregressive moving average (ARMA) models in time series data. This method offers improved performance and faster computation compared to existing algorithms, even with noisy data.

Area of Science:

  • Time series analysis
  • Signal processing
  • Mathematical modeling

Background:

  • Accurate modeling of time series data is crucial in various scientific fields.
  • Existing autoregressive moving average (ARMA) identification algorithms face limitations in parameter estimation accuracy and computational efficiency, particularly with noisy data or suboptimal model-order selection.
  • The fast orthogonal search (FOS) algorithm, while widely used, can struggle with parameter estimation in certain scenarios.

Purpose of the Study:

  • To develop a novel algorithm for identifying linear and nonlinear autoregressive (AR) moving average (MA) (ARMA) models in time series data.
  • To improve the accuracy and computational speed of ARMA model identification compared to existing methods.
  • To validate the algorithm's performance on both simulated and experimental physiological data.

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Main Methods:

  • Development of a new ARMA identification algorithm grounded in affine geometry principles.
  • The core innovation involves removing linearly dependent ARMA vectors from candidate pools.
  • Computer simulations were conducted using noiseless and noisy time series data, and the algorithm was applied to experimental renal blood flow and pressure data.

Main Results:

  • The new algorithm accurately estimates linear and nonlinear ARMA model parameters for noiseless time series data, even with incorrect initial model-order selection.
  • For noisy data, the algorithm outperforms the fast orthogonal search (FOS) algorithm for MA processes and performs comparably for ARMA processes.
  • The developed algorithm demonstrates faster computational time for parameter estimation than the FOS algorithm.
  • Application to physiological data yielded reliable and physiologically meaningful transfer function relationships between blood pressure and flow signals.

Conclusions:

  • The affine geometry-based ARMA identification algorithm provides accurate and efficient modeling of time series data.
  • This method surpasses existing algorithms like FOS in certain scenarios, particularly in terms of speed and robustness to noise.
  • The algorithm's successful application to physiological data highlights its practical utility in scientific research and analysis.