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Related Experiment Videos

Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure.

Epifanio Bagarinao1, Shunsuke Sato

  • 1Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka City, Japan. baggy@bpe.es.osaka-u.ac.jp

Annals of Biomedical Engineering
|April 19, 2002
PubMed
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The fast orthogonal search algorithm effectively estimates time-varying coefficients in vector autoregressive models and nonlinear parameters in vector nonlinear autoregressive models, even with short time series data.

Area of Science:

  • Signal Processing
  • Time Series Analysis
  • Machine Learning

Background:

  • Vector autoregressive (VAR) models are crucial for analyzing multivariate time series data.
  • Estimating time-varying and nonlinear parameters in VAR models presents significant challenges.
  • The fast orthogonal search (FOS) algorithm offers a potential solution for these estimation problems.

Purpose of the Study:

  • To review the derivation and applications of the fast orthogonal search (FOS) algorithm.
  • To examine the FOS algorithm's efficacy in estimating time-varying coefficients of vector autoregressive (VAR) processes.
  • To explore the extension of FOS for parameter estimation in vector nonlinear autoregressive (VNLAR) models.

Main Methods:

  • Review of the mathematical derivation of the fast orthogonal search (FOS) algorithm.

Related Experiment Videos

  • Application of FOS to estimate coefficient matrices of VAR models with time-varying coefficients using multiple realizations.
  • Computer simulations to assess the statistical properties of FOS estimates.
  • Extension of FOS to estimate parameters in vector nonlinear autoregressive (VNLAR) models, including nonlinear terms.
  • Testing FOS on chaotic time series data generated from the Lorenz equations.

    • Main Results:

    • The FOS algorithm provides accurate estimates of time-varying parameters in VAR models, even for short time series.
    • The standard deviation of FOS estimates follows a 1/√N pattern, characteristic of least-squares estimators.
    • FOS effectively estimates parameters in VNLAR models, successfully capturing nonlinear structures.
    • When applied to Lorenz equations data, FOS generated a model with the same chaotic attractor as the original system.

    Conclusions:

    • The fast orthogonal search (FOS) algorithm is a robust and effective tool for parameter estimation in both time-varying and nonlinear vector autoregressive models.
    • FOS demonstrates good performance with limited data length and accurately models complex dynamical systems.
    • The algorithm's versatility extends to various time series analysis applications, including those involving chaotic dynamics.