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Estimation of the year-on-year volatility and the unpredictability of the United States energy system

A Publisher Correction to this article was published on 12 March 2019

This article has been updated


Long-term projections of energy consumption, supply and prices heavily influence decisions regarding long-lived energy infrastructure. Predicting the evolution of these quantities over multiple years to decades is a difficult task. Here, we estimate year-on-year volatility and unpredictability over multi-decade time frames for many quantities in the US energy system using historical projections. We determine the distribution over time of the most extreme projection errors (unpredictability) from 1985 to 2014, and the largest year-over-year changes (volatility) in the quantities themselves from 1949 to 2014. Our results show that both volatility and unpredictability have increased in the past decade, compared to the three and two decades before it. These findings may be useful for energy decision-makers to consider as they invest in and regulate long-lived energy infrastructure in a deeply uncertain world.

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Fig. 1: Cumulative distribution functions of the projection errors for natural gas production separated by projection interval.
Fig. 2: Year-on-year changes for two energy quantities.
Fig. 3: Extreme changes for 17 energy quantities, from 1949 to 2014.
Fig. 4: Annual frequency of extreme errors for each quantity.
Fig. 5: The simulated probability of observing increases in the frequency of extreme errors for at least 15 of 17 quantities from 1995–2004 to 2005–2014.
Fig. 6: The maximum number of quantities for which all over-projected extreme errors occur in 2005–2014.

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Change history

  • 12 March 2019

    In the version of this Analysis originally published, the key for the size frequency in Fig. 4 was erroneously switched, and should have read 5% for the small black dot, and 50% for the large black dot. This has now been amended.


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We acknowledge and thank L. H. Kaack of Carnegie Mellon University for sharing the substantial task of data collection and harmonization, as well as J. Apt, M. G. Morgan, A. Davis, W. M. Griffin, E. Rubin, M. Small, G. Wong-Parodi, D. Armanios and S. Feinberg for their thoughtful feedback and advice. The final figures in the Supplementary Information benefited from editorial changes and suggestions from S. J. Davis. This material is based on work supported by the National Science Foundation Graduate Research Fellowship Program under grant no. DGE-1252522. This work was funded in part by the Center for Climate and Energy Decision Making (SES-0949710 and SES-1463492), through a cooperative agreement between the National Science Foundation and Carnegie Mellon University. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations



E.D.S. and I.M.L.A. secured project funding; E.D.S., I.M.L.A. and M.H. designed the study; E.D.S. analysed the data with iterative feedback from I.M.L.A. and M.H.; E.D.S. created the figures; E.D.S., I.M.L.A. and M.H. drafted and edited the manuscript.

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Correspondence to Inês M. L. Azevedo.

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Supplementary information

Supplementary Information

Supplementary Figures 1–16, Supplementary Tables 1–3, Supplementary Notes 1–12, Supplementary Discussion, Supplementary Methods and Supplementary References.

Supplementary Data 1

The data behind Figures 3 and 4

Supplementary Data 2

Cross-quantity and serial correlations within Annual Energy Outlook projections and projection errors, as well as cross-quantity correlations between historical values

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Sherwin, E.D., Henrion, M. & Azevedo, I.M.L. Estimation of the year-on-year volatility and the unpredictability of the United States energy system. Nat Energy 3, 341–346 (2018).

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