Abstract
Gibbs sampling for Bayesian VAR with mixed-frequency series draws latent high-frequency series and model parameters sequentially. Applying the multivariate Beveridge–Nelson (B–N) decomposition in each Gibbs step, one can simulate the joint posterior distribution of the B–N permanent and transitory components in latent and observable high-frequency series. This paper applies the method to mixed-frequency series of macroeconomic variables including quarterly real GDP to estimate the monthly natural rates and gaps of output, inflation, interest, and unemployment jointly. The resulting monthly real GDP and GDP gap are complementary coincident indices, measuring classical and deviation cycles, respectively.
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