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Updated: Sep 8, 2025

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Robust estimation using multivariate t innovations for vector autoregressive models via ECM algorithm.

Uchenna C Nduka1, Tobias E Ugah1, Chinyeaka H Izunobi2

  • 1Department of Statistics, University of Nigeria, Nsukka, Nigeria.

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|June 16, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new estimation method for vector autoregressive (VAR) models using multivariate t-distributions, offering improved efficiency and robustness over existing approaches for time series analysis.

Keywords:
EM algorithmsmaximum likelihood estimationmultivariate t distributionrobust estimationvector autoregressive model

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Area of Science:

  • Econometrics
  • Statistical Modeling
  • Time Series Analysis

Background:

  • Vector Autoregressive (VAR) models are widely used for time series analysis.
  • Multivariate t-distributions are more realistic than normal distributions for financial and economic data.
  • Existing maximum likelihood methods for VAR models with t-distributions face convergence issues.

Purpose of the Study:

  • To develop a robust and computationally efficient estimation procedure for VAR(p) models with multivariate t-error distributions.
  • To overcome the convergence problems associated with traditional maximum likelihood estimation.
  • To provide estimators that are easy to compute and perform well in practice.

Main Methods:

  • Utilizing the normal mean-variance mixture representation of the multivariate t-distribution.
  • Employing Expectation Maximization (EM)-based algorithms for computational ease.
  • Deriving explicit estimators as functions of sample observations.

Main Results:

  • The proposed estimators exhibit negligible bias and superior efficiency compared to least-squares methods.
  • The developed method demonstrates robustness against deviations from the assumed distribution.
  • The estimators are computationally straightforward, relying on explicit functions of data.

Conclusions:

  • The new estimation procedure offers a practical and reliable alternative for VAR models with t-distributions.
  • The robustness and efficiency of the proposed estimators make them advantageous for real-world applications.
  • The method provides a valuable tool for analyzing complex time series data with heavy-tailed errors.