Climate Time Series Analysis: Classical Statistical and Bootstrap Methods

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Trend analysis of climate time series: A review of methods (2019, background): “The topic of uncertain timescales has not been a focus of statisticians in the past, and the methodology of quantitatively assessing the influence of timescale uncertainties (Mudelsee (2010) is, at the time of writing (mid 2018), not very far advanced.”
More accurate, calibrated bootstrap confidence intervals for estimating the correlation between two time series (2014, methodology): “The bivariate AR(1) process for uneven spacing is given by (Mudelsee 2010, Ch. 7.6) X (1) = E XN(0, 1)(1), Y (1) = E YN(0, 1)(1), X (i) = exp {− [T (i) − T (i − 1)] /τX } · X (i − 1) +E XN(0, 1−exp{−2[T (i)−T (i−1)]/τX })(i), i = 2, . . . , n, Y (i) = exp {− [T (i) − T (i − 1)] /τY } · Y (i − 1) +E…”
REDFIT-X: Cross-spectral analysis of unevenly spaced paleoclimate time series (2016, background): “The frequency fk is in the range from the fundamental frequency ¯ = ( ¯)f nd1/ to the average Nyquist frequency = ( ¯)f d1/ 2Nyq , where n is the number of data points and ¯ = [ ( ) − ( )] ( − )d t n t n1 / 1 is the average spacing of the time series (Mudelsee, 2010).”