R2 Bounds for Predictive Models: What Univariate Properties Tell us About Multivariate Predictability |
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| Authors: | James Mitchell Donald Robertson Stephen Wright |
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| Institution: | 1. Warwick Business School, University of Warwick, Coventry CV4 7AL, United Kingdom (James.Mitchell@wbs.ac.uk);2. Faculty of Economics, University of Cambridge, Cambridge CB3 9DD, United Kingdom (dr10011@cam.ac.uk);3. Department of Economics, Maths &4. Statistics, Birkbeck College, University of London, London W1E 7HX, United Kingdom (s.wright@bbk.ac.uk) |
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| Abstract: | ABSTRACTA 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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| Keywords: | Autoregressive moving average representations Forecasting Macroeconomic models Nonfundamental representations Predictive regressions Time-varying ARMA |
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