VAR models with an index structure: A survey with new results

TL;DR

This survey reviews recent advances in multivariate autoregressive index models, highlighting their connections to VAR and DFM approaches, and introduces new results on model extensions and insights.

Contribution

The paper provides a comprehensive review of recent developments in MAI models, including new theoretical insights and extensions such as stochastic volatility and high-dimensionality.

Findings

MAI models link VAR and DFM approaches effectively.

Recent extensions include stochastic volatility and time-varying parameters.

New insights and a novel model are introduced.

Abstract

The main aim of this paper is to review recent advances in the multivariate autoregressive index model [MAI], originally proposed by Reinsel (1983), and their applications to economic and financial time series. MAI has recently gained momentum because it can be seen as a link between two popular but distinct multivariate time series approaches: vector autoregressive modeling [VAR] and the dynamic factor model [DFM]. Indeed, on the one hand, the MAI is a VAR model with a peculiar reduced-rank structure; on the other hand, it allows for identification of common components and common shocks in a similar way as the DFM. The focus is on recent developments of the MAI, which include extending the original model with individual autoregressive structures, stochastic volatility, time-varying parameters, high-dimensionality, and cointegration. In addition, new insights on previous contributions and a novel model are also provided.