Vector AutoRegressive Moving Average Models: A Review

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.