Persistence matters: Estimation of the statistical significance of paleoclimatic reconstruction statistics from autocorrelated time series


Marc Macias-Fauria*, Aslak Grinsted, Samuli Helama & Jari Holopainen


Dendrochronologia 30 (2012) 179-187.

*Corresponding author


Proxy data forms natural time series used to lengthen instrumental climatic records, and may contain a significant portion of autocorrelation. Increased serial correlation limits the number of independent observations, not satisfying the assumptions of conventional statistical methods. We estimate the significance of calibration and verification statistics used in dendroclimatic reconstructions by combining Monte-Carlo iterations with frequency (Ebisuzaki) or time (Burg) domain time series modelling. Significance tests are presented for Coefficient of Determination (R2), Coefficient of Correlation (r2), Reduction of Error (RE) and Coefficient of Error (CE) for time series ranging from very low to very high autocorrelation. Increased autocorrelation implies higher occurrences of relatively high but spurious reconstruction statistics. Ebisuzaki time series modelling shows greater robustness and its use is recommended over Burg's method, which penalizes the restriction in the number of autocorrelation coefficients imposed by the Akaike Information Criterion. Positive RE and CE values, traditionally viewed as successful reconstruction statistics, are not necessarily significant and depend on the temporal structure of the time series used. This approach is further implemented successfully to compute confidence intervals based on the temporal structure of the residuals of the transfer function. A Matlab® package and a Windows executable file for non-Matlab® users are provided to perform the described analyses.


Abovementioned paper describes two programs: reconstats and correl. Here we offer you a possibility to download Windows executable packages that you may then use to run the programs to calibrate and vefiry our own data. Before using, please see README.TXT file. Please cite the paper if your research benefitted from these softwares!

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Other papers using the algoritms

Helama S., Nielsen J. K., Macias Fauria M. & Valovirta I. 2009: A fistful of shells: amplifying sclerochronological and palaeoclimate signals from molluscan death assemblages. Geological Magazine 146: 917-930.

Macias Fauria M.
, Grinsted A., Helama S., Moore J., Timonen M., Martma T., Isaksson E. & Eronen M. 2010: Unprecedented low twentieth century winter sea ice extent in the Western Nordic Seas since A.D. 1200. Climate Dynamics 34: 781-795.

Helama S., Macias Fauria M., Mielikäinen K., Timonen M. & Eronen M. 2010: Sub-Milankovitch solar forcing of past climates: mid and late Holocene perspectives. Geological Society of America Bulletin 122: 1981-1988.

Helama S., Seppä, H., Birks, H. J. B. & Bjune, A. E. 2010: Reconciling pollen-stratigraphical and tree-ring evidence for high- and low-frequency temperature variability in the past millennium. Quaternary Science Reviews 29: 3905-3918.

Helama S. & Holopainen J. 2012: Spring temperature variability relative to the North Atlantic Oscillation and sunspots - A correlation analysis with a Monte Carlo implementation. Palaeogeography, Palaeoclimatology, Palaeoecology 326-328: 128-134.

Läänelaid A., Helama S., Kull A., Timonen M. & Jaagus, J. 2012: Common growth signal and spatial synchrony of the chronologies of tree-rings from pines in the Baltic Sea region over the last nine centuries. Dendrochronologia 30: 147-155.