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significantly related to it and further displayed time-dependent structure in the residuals.

However, the 7 other regressions were significant at the 5% level (Table 3) and

displayed normally distributed residuals. The boxplot of the probabilities tended to

confirm that BFT time series were, in general, significantly related to D’Arrigo’s time

series, but this was less obvious than with Jones’ time series (Fig. 5c). Most of the fits

of the GLS model led to lower slope coefficients (from -2.76 to 0.86, Table 3) and to a

significant drop in the strength of the relationship (only 2 of the 14 regressions

remained significant, Table 3). This again shows that long-term trends were the most

common feature to BFT, Jones’ and D’Arrigo’s time series. These findings were

confirmed by the highly negative correlation coefficients, among which 100% (for

Jones’ proxy) and about 80% (for D’Arrigo’s proxy) were significant at the 5% level for

both corrected and non-corrected correlation analyses (Table 3).

The spectra of the four local temperature time series were also dominated by long-

term variability, being highly similar to those of the BFT time series (Fig. 4). 23

regressions between BFT and local temperature were significant at the 1% level and the

th
24 one at the 5% level (Table 3). The boxplots of the probabilities displayed

unambiguous results for all the four temperature time series (Fig. 5d). All regressions

exhibited downward slopes (among which 12 were particularly strong, with slope < -

0.5, Table 3). The GLS regressions led to lower and non-significant relationships in

86% of the cases and weak slopes coefficients (from -0.30 to 0.26, Table 3). This again

indicated that long-term signals were common to BFT and local temperature time series.

Finally, correlation analyses confirmed the strong and negative relationships between

BFT and local temperature. All the correlation coefficients were significant at 5% (and

for the most at 1%), even when correction for multiple testing was applied.

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