VAR Models with an Index Structure: A Survey with New Results

The main aim of this paper is to review recent advances in the multivariate autoregressive index model [MAI] 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, MAI is a VAR model with a peculiar reduced-rank structure that can lead to a significant dimension reduction; on the other hand, it allows for the identification of common components and common shocks in a similar way as the DFM. Our 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 co-integration. In addition, some gaps in the literature are filled by providing new results on the representation theory underlying previous contributions, and a novel model is provided.