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Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction

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  • Matteo Mogliani
  • Anna Simoni

Abstract

We propose a new approach to mixed-frequency regressions in a high-dimensional environment that resorts to Group Lasso penalization and Bayesian techniques for estimation and inference. In particular, to improve the prediction properties of the model and its sparse recovery ability, we consider a Group Lasso with a spike-and-slab prior. Penalty hyper-parameters governing the model shrinkage are automatically tuned via an adaptive MCMC algorithm. We establish good frequentist asymptotic properties of the posterior of the in-sample and out-of-sample prediction error, we recover the optimal posterior contraction rate, and we show optimality of the posterior predictive density. Simulations show that the proposed models have good selection and forecasting performance in small samples, even when the design matrix presents cross-correlation. When applied to forecasting U.S. GDP, our penalized regressions can outperform many strong competitors. Results suggest that financial variables may have some, although very limited, short-term predictive content.

Suggested Citation

  • Matteo Mogliani & Anna Simoni, 2019. "Bayesian MIDAS Penalized Regressions: Estimation, Selection, and Prediction," Papers 1903.08025, arXiv.org, revised Jun 2020.
  • Handle: RePEc:arx:papers:1903.08025
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    Cited by:

    1. Andrii Babii & Eric Ghysels & Jonas Striaukas, 2022. "Machine Learning Time Series Regressions With an Application to Nowcasting," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(3), pages 1094-1106, June.
    2. Caroline Jardet & Baptiste Meunier, 2022. "Nowcasting world GDP growth with high‐frequency data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(6), pages 1181-1200, September.
    3. Tibor Szendrei & Arnab Bhattacharjee & Mark E. Schaffer, 2024. "MIDAS-QR with 2-Dimensional Structure," Papers 2406.15157, arXiv.org.
    4. Matteo Mogliani & Anna Simoni, 2024. "Bayesian Bi-level Sparse Group Regressions for Macroeconomic Density Forecasting," Papers 2404.02671, arXiv.org, revised Nov 2024.
    5. Alexandra Bozhechkova & Urmat Dzhunkeev, 2024. "CLARA and CARLSON: Combination of Ensemble and Neural Network Machine Learning Methods for GDP Forecasting," Russian Journal of Money and Finance, Bank of Russia, vol. 83(3), pages 45-69, September.
    6. Jad Beyhum & Jonas Striaukas, 2023. "Factor-augmented sparse MIDAS regressions with an application to nowcasting," Papers 2306.13362, arXiv.org, revised Nov 2024.
    7. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
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    9. Ferrara, Laurent & Mogliani, Matteo & Sahuc, Jean-Guillaume, 2022. "High-frequency monitoring of growth at risk," International Journal of Forecasting, Elsevier, vol. 38(2), pages 582-595.
    10. Zheng, Tingguo & Fan, Xinyue & Jin, Wei & Fang, Kuangnan, 2024. "Words or numbers? Macroeconomic nowcasting with textual and macroeconomic data," International Journal of Forecasting, Elsevier, vol. 40(2), pages 746-761.
    11. Iacopini, Matteo & Poon, Aubrey & Rossini, Luca & Zhu, Dan, 2023. "Bayesian mixed-frequency quantile vector autoregression: Eliciting tail risks of monthly US GDP," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    12. Kohns, David & Potjagailo, Galina, 2023. "Flexible Bayesian MIDAS: time‑variation, group‑shrinkage and sparsity," Bank of England working papers 1025, Bank of England.
    13. Richard Schnorrenberger & Aishameriane Schmidt & Guilherme Valle Moura, 2024. "Harnessing Machine Learning for Real-Time Inflation Nowcasting," Working Papers 806, DNB.
    14. Helena Chuliá & Ignacio Garrón & Jorge M. Uribe, 2022. ""Monitoring daily unemployment at risk"," IREA Working Papers 202211, University of Barcelona, Research Institute of Applied Economics, revised Jul 2022.
    15. Ana Beatriz Galvão & Michael Owyang, 2022. "Forecasting low‐frequency macroeconomic events with high‐frequency data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1314-1333, November.
    16. Alain Hecq & Marie Ternes & Ines Wilms, 2023. "Hierarchical Regularizers for Reverse Unrestricted Mixed Data Sampling Regressions," Papers 2301.10592, arXiv.org, revised Nov 2024.
    17. Ziwei Mei & Zhentao Shi, 2022. "On LASSO for High Dimensional Predictive Regression," Papers 2212.07052, arXiv.org, revised Jan 2024.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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