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Vector AutoRegressive Moving Average Models: A Review.

Marie-Christine Düker1, David S Matteson2, Ruey S Tsay3

  • 1Department of Statistics and Data Science Friedrich-Alexander Universität Erlangen-Nürnberg Erlangen Germany.

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View abstract on PubMed

Summary
This summary is machine-generated.

Vector AutoRegressive Moving Average (VARMA) models offer advanced insights into multiple time series dynamics. This review explores VARMA models, highlighting their advantages over Vector AutoRegressive (VAR) models for improved analysis and forecasting.

Keywords:
Granger causalityforecastingidentificationmodel checkingmultivariate time series

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Area of Science:

  • Econometrics
  • Time Series Analysis
  • Statistical Modeling

Background:

  • Vector AutoRegressive Moving Average (VARMA) models are a versatile class for analyzing multivariate time series.
  • Despite their capabilities, Vector AutoRegressive (VAR) models are more frequently used in empirical applications.
  • The reasons for VAR's dominance over VARMA models in practice are not fully understood.

Purpose of the Study:

  • To provide a comprehensive resource on the advantages and capabilities of VARMA models.
  • To guide researchers and practitioners in utilizing VARMA models effectively.
  • To address the underutilization of VARMA models in empirical research.

Main Methods:

  • Review of classical and modern identification schemes for VARMA models.
  • Discussion of estimation, specification, and diagnostic techniques for VARMA models.
  • Exploration of practical applications including Granger Causality, forecasting, and structural analysis.

    • Main Results:

    • VARMA models present unique identification challenges but offer superior analytical power.
    • Effective methods for estimation, specification, and diagnosis are available for VARMA models.
    • VARMA models provide significant advantages in Granger Causality, forecasting, and structural analysis.

    Conclusions:

    • VARMA models possess significant potential for time series analysis that is often underappreciated.
    • Addressing identification and estimation challenges can facilitate wider adoption of VARMA models.
    • Further research into VARMA extensions can enhance their practical utility and application scope.