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High-dimensional macroeconomic forecasting using message passing algorithms

Author

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  • Korobilis, Dimitris

Abstract

This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous predictors, as an equivalent high-dimensional static regression problem with thousands of covariates. Inference in this specification proceeds using Bayesian hierarchical priors that shrink the high-dimensional vector of coefficients either towards zero or time-invariance. Second, it introduces the frameworks of factor graphs and message passing as a means of designing efficient Bayesian estimation algorithms. In particular, a Generalized Approximate Message Passing (GAMP) algorithm is derived that has low algorithmic complexity and is trivially parallelizable. The result is a comprehensive methodology that can be used to estimate time-varying parameter regressions with arbitrarily large number of exogenous predictors. In a forecasting exercise for U.S. price inflation this methodology is shown to work very well.

Suggested Citation

  • Korobilis, Dimitris, 2019. "High-dimensional macroeconomic forecasting using message passing algorithms," MPRA Paper 96079, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:96079
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    File URL: https://mpra.ub.uni-muenchen.de/96079/1/MPRA_paper_96079.pdf
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    References listed on IDEAS

    as
    1. Korobilis, Dimitris, 2013. "Hierarchical shrinkage priors for dynamic regressions with many predictors," International Journal of Forecasting, Elsevier, vol. 29(1), pages 43-59.
    2. Blix, Mårten, 1999. "Forecasting Swedish Inflation With a Markov Switching VAR," Working Paper Series 76, Sveriges Riksbank (Central Bank of Sweden).
    3. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    4. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
    5. Giordani, Paolo & Kohn, Robert, 2008. "Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 66-77, January.
    6. Jan J. J. Groen & Richard Paap & Francesco Ravazzolo, 2013. "Real-Time Inflation Forecasting in a Changing World," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 29-44, January.
    7. Joshua C.C. Chan & Gary Koop & Roberto Leon-Gonzalez & Rodney W. Strachan, 2012. "Time Varying Dimension Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 358-367, January.
    8. Davide Pettenuzzo & Allan Timmermann, 2017. "Forecasting Macroeconomic Variables Under Model Instability," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 183-201, April.
    9. Jouchi Nakajima & Mike West, 2013. "Bayesian Analysis of Latent Threshold Dynamic Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 151-164, April.
    10. Kalli, Maria & Griffin, Jim E., 2014. "Time-varying sparsity in dynamic regression models," Journal of Econometrics, Elsevier, vol. 178(2), pages 779-793.
    11. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    12. Cooley, Thomas F & Prescott, Edward C, 1976. "Estimation in the Presence of Stochastic Parameter Variation," Econometrica, Econometric Society, vol. 44(1), pages 167-184, January.
    13. repec:taf:jnlasa:v:112:y:2017:i:517:p:137-168 is not listed on IDEAS
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    Cited by:

    1. Arefiev, Nikolay & Khabibullin, Ramis, 2018. "Bayesian identification of structural vector autoregression models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 49, pages 115-142.
    2. George Kapetanios & Fotis Papailias, 2018. "Big Data & Macroeconomic Nowcasting: Methodological Review," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-12, Economic Statistics Centre of Excellence (ESCoE).
    3. Dimitris Korobilis, 2018. "Machine Learning Macroeconometrics: A Primer," Working Paper series 18-30, Rimini Centre for Economic Analysis.

    More about this item

    Keywords

    high-dimensional inference; factor graph; Belief Propagation; Bayesian shrinkage; time-varying parameter model;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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