Abstract: The study considers a vector autoregressive model for high-dimensional mixed frequency data, where selective time series are collected at different frequencies. The high-frequency series are expanded and modeled as multiple time series to match the low-frequency sampling of the corresponding low-frequency series. This leads to an expansion of the parameter space, and poses challenges for estimation and inference in settings with a limited number of observations. We address these challenges by considering specific structural relationships in the representation of the high-frequency series, together with the sparsity of the model parameters by introducing spike-and-Gaussian slab prior distributions. In contrast to existing observation-driven methods, the proposed Bayesian approach accommodates general sparsity patterns, and makes a data-driven choice of them. Under certain regularity conditions, we establish the consistency for the posterior distribution under high-dimensional scaling. Applications to synthetic and real data illustrate the efficacy of the resulting estimates and corresponding credible intervals.

Key words and phrases: High dimensional data, mixed frequencies, nowcasting, pseudo-likelihood, spike and slab prior, strong selection consistency.