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

Abstract: The main aim of this paper is to review recent advances in the multivariate autoregressive index model [MAI], originally proposed by <cite>reinsel1983some</cite>, 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.