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R2 Bounds for Predictive Models: What Univariate Properties Tell us About Multivariate Predictability

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  • James Mitchell
  • Donald Robertson
  • Stephen Wright

Abstract

A long-standing puzzle in macroeconomic forecasting has been that a wide variety of multivariate models have struggled to out-predict univariate models consistently. We seek an explanation for this puzzle in terms of population properties. We derive bounds for the predictive R2 of the true, but unknown, multivariate model from univariate ARMA parameters alone. These bounds can be quite tight, implying little forecasting gain even if we knew the true multivariate model. We illustrate using CPI inflation data. Supplementary materials for this article are available online.

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  • James Mitchell & Donald Robertson & Stephen Wright, 2019. "R2 Bounds for Predictive Models: What Univariate Properties Tell us About Multivariate Predictability," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 681-695, October.
    • Handle: RePEc:taf:jnlbes:v:37:y:2019:i:4:p:681-695
    DOI: 10.1080/07350015.2017.1415909
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    4. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    5. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
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    Cited by:

    1. Ana Beatriz Galvão & James Mitchell, 2019. "Measuring Data Uncertainty: An Application using the Bank of England's "Fan Charts" for Historical GDP Growth," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2019-08, Economic Statistics Centre of Excellence (ESCoE).
    2. Mihaela-Eugenia VASILACHE, 2018. "Forecasting the Trend of Art Market," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 6(1), pages 82-93, June.
    3. Zhang, Bo & Chan, Joshua C.C. & Cross, Jamie L., 2020. "Stochastic volatility models with ARMA innovations: An application to G7 inflation forecasts," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1318-1328.
    4. Tommaso Proietti, 2021. "Predictability, real time estimation, and the formulation of unobserved components models," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 433-454, April.
    5. Julien Champagne & Guillaume Poulin‐Bellisle & Rodrigo Sekkel, 2020. "Introducing the Bank of Canada staff economic projections database," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 114-129, January.
    6. Duc Do, Nguyen, 2024. "Money/asset ratio as a predictor of inflation," The Quarterly Review of Economics and Finance, Elsevier, vol. 97(C).
    7. Nguyen Duc Do, 2025. "Using a Wage–Price‐Setting Model to Forecast US Inflation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(2), pages 803-832, March.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • 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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