Estimation of the statistical significance of paleoclimatic
reconstruction statistics from autocorrelated time series
Marc Macias-Fauria*, Aslak Grinsted, Samuli Helama & Jari
Dendrochronologia 30 (2012) 179-187.
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
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papers using the algoritms
Nielsen J. K., Macias Fauria M.
& Valovirta I. 2009: A fistful of shells:
amplifying sclerochronological and palaeoclimate signals from molluscan
assemblages. Geological Magazine
Macias Fauria M.,
A., Helama S., Moore
J., Timonen M., Martma T., Isaksson
E. & Eronen
M. 2010: Unprecedented low twentieth century winter sea ice extent in
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:
late Holocene perspectives. Geological
Society of America Bulletin 122: 1981-1988.
Seppä, H., Birks, H. J. B. & Bjune, A. E. 2010: Reconciling
pollen-stratigraphical and tree-ring evidence for high- and
temperature variability in the past millennium. Quaternary
& Holopainen J. 2012:
Spring temperature variability relative to the North
Atlantic Oscillation and sunspots - A correlation analysis with a Monte
Palaeoclimatology, Palaeoecology 326-328:
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