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

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  • Gianluca Cubadda

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.

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  • Gianluca Cubadda, 2024. "VAR models with an index structure: A survey with new results," Papers 2412.11278, arXiv.org, revised Sep 2025.
    • Handle: RePEc:arx:papers:2412.11278
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