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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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    1. 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.
    2. Joshua C. C. Chan & Gary Koop & Simon M. Potter, 2013. "A New Model of Trend Inflation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 94-106, January.
    3. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    4. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    5. 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.
    6. 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.
    7. Lars Peter Hansen & Thomas J. Sargent, 2013. "Recursive Models of Dynamic Linear Economies," Economics Books, Princeton University Press, edition 1, number 10141.
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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. repec:wrk:wrkemf:35 is not listed on IDEAS
    3. 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.
    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. 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.
    6. 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.
    7. repec:wrk:wrkemf:24 is not listed on IDEAS

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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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