Environmental and Ecological Statistics

, Volume 22, Issue 1, pp 105–126 | Cite as

Specification and estimation of the transfer function in dendroclimatological reconstructions

  • Maximilian AuffhammerEmail author
  • Bo LiEmail author
  • Brian Wright
  • Seung-Jick Yoo


We identify two issues with the reverse regression approach as implemented in several classic reconstructions of past climate fluctuations from dendroclimatologcical data series. First, instead of estimating the causal relationship between the proxy, which is measured with significant error, as function of climate and formally inverting the relationship, most papers estimate the inverted relationship directly. This leads to biased coefficients and reconstructions with artificially low variance. Second, we show that inversion of the relationship is often done incorrectly when the underlying causal relationship is dynamic in nature. We show analytically as well as using Monte Carlo experiments and actual tree ring data, that the reverse regression method results in biased coefficients, reconstructions with artificially low variance and overly smooth reconstructions. We further demonstrate that correct application of the inverse regression method is preferred. However, if the measurement error in the tree ring index is significant, neither method provides reliable reconstructions.


Climate change Climate variability Inversion Paleoclimatic data Reconstruction method 



Auffhammer thanks the Giannini Foundation for support. Lis research was partially supported by the NSF Grant DMS-1007686. The authors thank the Guest Editor and two anonymous referees for their helpful comments and suggestions.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.University of Illinois at Urbana-ChampaignChampaignUSA
  3. 3.Greenhouse Gas Inventory & Research Center of KoreaJongno-guKorea

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