Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors. (English) Zbl 1452.62890

J. Econom. 212, No. 1, 137-154 (2019); corrigendum ibid. 227, No. 2, 506-512 (2022).
Summary: Recent research has shown that a reliable vector autoregression (VAR) for forecasting and structural analysis of macroeconomic data requires a large set of variables and modeling time variation in their volatilities. Yet, there are no papers that provide a general solution for combining these features, due to computational complexity. Moreover, homoskedastic Bayesian VARs for large data sets so far restrict substantially the allowed prior distributions on the parameters. In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time-varying volatilities and general priors. We show that indeed empirically the new estimation procedure performs well in applications to both structural analysis and out-of-sample forecasting.


62P20 Applications of statistics to economics
62F15 Bayesian inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)


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[1] Banbura, M.; Giannone, D.; Reichlin, L., Large bayesian vector autoregressions, J. Appl. Econometrics, 25, 71-92, (2010)
[2] Bernanke, B.; Boivin, J.; Eliasz, P., Measuring the effects of monetary policy: a factor-augmented vector autoregressive (FAVAR) approach, Quar. J. Econ., 120, 387-422, (2005)
[3] Bognanni, Mark, 2018. A class of time-varying parameter structural VARs for inference under exact or partial identification. Federal Reserve Bank of Cleveland Working Paper, 18-11. myehosthttp://dx.doi.org/10.26509/frbc-wp-201811.
[4] Campbell, J.; Shiller, R., Cointegration and tests of present value models, J. Political Econ., 95, 1062-1088, (1987)
[5] Carriero, A.; Clark, T.; Marcellino, M., Bayesian VARs: specification choices and forecast accuracy, J. Appl. Econometrics, 30, 46-73, (2015)
[6] Carriero, A.; Clark, T.; Marcellino, M., Common drifting volatility in large Bayesian VARs, J. Bus. Econom. Statist., 34, 375-390, (2016)
[7] Carriero, A.; Clark, T.; Marcellino, M., Measuring uncertainty and its effects on the economy, Rev. Econ. Stat., 100, 799-815, (2017)
[8] Chan, J., Large Bayesian VARs: a flexible Kronecker error covariance structure, J. Bus. Econom. Statist., 1-12, (2018)
[9] Chib, S.; Greenberg, E., Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models, J. Econometrics, 68, 339-360, (1995) · Zbl 0833.62103
[10] Clark, T., Real-time density forecasts from Bayesian Vector Autoregressions with stochastic volatility, J. Bus. Econom. Statist., 29, 327-341, (2011) · Zbl 1219.91106
[11] Clark, T.; Ravazzolo, F., Macroeconomic forecasting performance under alternative specifications of time-varying volatility, J. Appl. Econometrics, 30, 551-575, (2015)
[12] Cogley, T.; Morozov, S.; Sargent, T., Bayesian fan charts for U.K. inflation: forecasting and sources of uncertainty in an evolving monetary system, J. Econ. Dyn. Control, 29, 1893-1925, (2005) · Zbl 1198.91174
[13] Cogley, T.; Sargent, T., Drifts and volatilities: monetary policies and outcomes in the post-WWII US, Rev. Econ. Dyn., 8, 262-302, (2005)
[14] D’Agostino, D.; Gambetti, L.; Giannone, D., Macroeconomic forecasting and structural change, J. Appl. Econometrics, 28, 82-101, (2013)
[15] Del Negro, M.; Schorfheide, F., Priors from general equilibrium models for VARs, Internat. Econom. Rev., 45, 643-673, (2004)
[16] Diebold, F., Comparing predictive accuracy, twenty years later: a personal perspective on the use and abuse of Diebold-Mariano tests, J. Bus. Econ. Stat., 33, 1-9, (2015)
[17] Geweke, J.; Whiteman, C., Bayesian forecasting, (Elliott, G.; Granger, C. W.J.; Timmermann, A., Handbook of Economic Forecasting, Volume 1, (2006), Elsevier), 3-80
[18] Giannone, D.; Lenza, M.; Primiceri, G., Prior selection for vector autoregressions, Rev. Econ. Stat., 97, 436-451, (2015)
[19] Giannone, D.; Lenza, M.; Primiceri, G., Priors for the long run, J. Amer. Statist. Assoc., 1-16, (2018)
[20] Ingram, B.; Whiteman, C., Supplanting the ‘Minnesota’ prior: forecasting macroeconomic time series using real business cycle model priors, J. Monetary Econ., 34, 497-510, (1994)
[21] Jacquier, E.; Polson, N.; Rossi, P., Bayesian analysis of stochastic volatility models, J. Bus. Econom. Statist., 20, 69-87, (1994)
[22] Kadiyala, K.; Karlsson, S., Forecasting with generalized Bayesian vector autoregressions, J. Forecast., 12, 365-378, (1993)
[23] Kadiyala, K.; Karlsson, S., Numerical methods for estimation and inference in Bayesian VAR models, J. Appl. Econometrics, 12, 99-132, (1997)
[24] Karlsson, S., Forecasting with bayesian vector autoregression, (Elliott, G.; Timmermann, A., Handbook of Economic Forecasting, Volume 2, (2013), Elsevier), 791-897
[25] Kim, S.; Shephard, N.; Chib, S., Stochastic volatility: likelihood inference and comparison with ARCH models, Rev. Econom. Stud., 65, 361-393, (1998) · Zbl 0910.90067
[26] Koop, G., Forecasting with medium and large Bayesian VARs, J. Appl. Econometrics, 28, 177-203, (2013)
[27] Koop, G.; Korobilis, D., Large time-varying parameter VARs, J. Econometrics, 177, 185-198, (2013) · Zbl 1288.62127
[28] Koop, G.; Korobilis, D.; Pettenuzzo, D., Bayesian compressed vector autoregressions, J. Econometrics, (2018), forthcoming. · Zbl 1452.62934
[29] Korobilis, D.; Pettenuzzo, D., Adaptive hierarchical priors for high-dimensional vector autoregressions, J. Econometrics, 212, 241-271, (2019), https://ideas.repec.org/p/rim/rimwps/18-21.html
[30] Litterman, R., Forecasting with Bayesian vector autoregressions — five years of experience, J. Bus. Econom. Statist., 4, 25-38, (1986)
[31] McCracken, M.; Ng, S., FRED-MD: a monthly database for macroeconomic research, J. Bus. Econom. Statist., 34, 574-589, (2016)
[32] Philipov, A.; Glickman, M., Multivariate stochastic volatility via Wishart processes, J. Bus. Econom. Statist., 24, 313-328, (2006) · Zbl 1113.62131
[33] Primiceri, G., Time-varying structural vector autoregressions and monetary policy, Rev. Econom. Stud., 72, 821-852, (2005) · Zbl 1106.91047
[34] Rothenberg, T., A Bayesian analysis of simultaneous equation systemsReport 6315, (1963), Econometric Institute, Netherlands School of Economics: Econometric Institute, Netherlands School of Economics Rotterdam
[35] Shin, M.; Zhong, M., A new approach to identifying the real effects of uncertainty shocks, J. Bus. Econom. Statist., 1-13, (2018)
[36] Sims, C., A nine-variable probabilistic macroeconomic forecasting model, (Stock, J.; Watson, M., Business Cycles, Indicators and Forecasting, (1993), University of Chicago Press), 179-212
[37] Sims, C.; Zha, T., Bayesian methods for dynamic multivariate models, Internat. Econom. Rev., 39, 949-968, (1998)
[38] Villani, M., Steady-state priors for vector autoregressions, J. Appl. Econometrics, 24, 630-650, (2009)
[39] Waggoner, D.; Zha, T., A Gibbs sampler for structural vector autoregressions, J. Econom. Dynam. Control, 28, 349-366, (2003) · Zbl 1187.62149
[40] Zellner, A., An Introduction To Bayesian Inference in Econometrics, (1973), Wiley: Wiley New York
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