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Abstract:
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In the recent past, considerable advances have been made in the research on Vector Autoregressive (VAR) models. It is widely used for simultaneous forecasting of multiple temporally observed variables and has got many applications in macroeconomics, finance and other areas. We often find economic data collected at various frequencies. Though some studies have been done in the recent years on mixed frequency VAR models, not much theory is yet developed on the posterior distribution of mixed-frequency Bayesian VAR models in high-dimensional setup. Here we consider a mixed-frequency VAR model speci?ed at the lowest sampling frequency; treating high frequency observations as different series occurring at the low frequency. To introduce sparsity in the model coefficients, we use spike and slab prior, which is a mixture of a degenerate distribution at zero (spike) and Gaussian distribution(slab), for the autoregressive coefficient matrix. Under standard regularity assumptions, we establish posterior consistency for this prior when the dimension of the VAR model grows with the sample size. The efficiency of the proposed estimation method is demonstrated on synthetic and real data sets.
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