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Vector AutoRegressive Moving Average Models: A Review

Marie-Christine Düker, David S. Matteson, Ruey S. Tsay, Ines Wilms

arXiv 28 Jun 2024 · Statistics — Methodology · publishedWiley Interdisciplinary Reviews Computational Statistics (2025) · 19 citations (OpenAlex)

arXiv:2406.19702 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Vector AutoRegressive Moving Average (VARMA) models form a powerful and general model class for analyzing dynamics among multiple time series. While VARMA models encompass the Vector AutoRegressive (VAR) models, their popularity in empirical applications is dominated by the latter. Can this phenomenon be explained fully by the simplicity of VAR models? Perhaps many users of VAR models have not fully appreciated what VARMA models can provide. The goal of this review is to provide a comprehensive resource for researchers and practitioners seeking insights into the advantages and capabilities of VARMA models. We start by reviewing the identification challenges inherent to VARMA models thereby encompassing classical and modern identification schemes and we continue along the same lines regarding estimation, specification and diagnosis of VARMA models. We then highlight the practical utility of VARMA models in terms of Granger Causality analysis, forecasting and structural analysis as well as recent advances and extensions of VARMA models to further facilitate their adoption in practice. Finally, we discuss some interesting future research directions where VARMA models can fulfill their potentials in applications as compared to their subclass of VAR models.

Citation extraction

210
references
272
in-text mentions
210
distinct cited
11
self-citations
14,082
main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Lütkepohl, H (2005) New introduction to multiple time series analysis1.00074100%
2Akaike, H (1976) Canonical correlation analysis of time series and the use of an information criterion0.92843100%
3Tiao, G. and Tsay, R (1989) Model specification in multivariate time series self0.87482100%
4Tsay, R (2013) Multivariate Time Series Analysis: with R and Financial Applications self0.87482100%
5Tsay, R. and Wood, D (2022) MTS: All-purpose toolkit for analyzing multivariate time series (mts) and estimating multivariate volatility models self0.84333100%
6Poskitt, D (1992) Identification of echelon canonical forms for vector linear processes using least squares0.81142100%
7Dufour, J.-M. and Pelletier, D (2022) Practical methods for modeling weak VARMA processes: Identification, estimation and specification with a macroeconomic application0.73732100%
8Tiao, G. and Box, G (1981) Modeling multiple time series with applications0.73732100%
9Tsay, R (1989) Identifying multivariate time series models self0.73732100%
10Wilms, I., Basu, S., Bien, J., and Matteson, D (2023) Sparse identification and estimation of large-scale vector autoregressive moving averages self0.73732100%

Showing the top 10 of 210 scored citations.