Empirical Economics

, Volume 51, Issue 4, pp 1415–1441 | Cite as

The Beveridge–Nelson decomposition of mixed-frequency series

An application to simultaneous measurement of classical and deviation cycles


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.


Bayesian Gap Growth cycle Monthly GDP Natural rate Trend–cycle decomposition 

JEL classification

C11 C32 C43 C82 E32 



I thank two referees, Manabu Asai, David Garcia-Leon, and Yohei Yamamoto for useful comments. This work was supported by JSPS KAKENHI Grant Number 23530255.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of EconomicsKonan UniversityKobeJapan

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