If these plots show annually-resolved data, presumably these have been interpolated from coarse resolution series, and are somewhat artificial in nature(?) According to the ACF plots, one could presumably obtain quasi-independent data points by using only one of every ~70 values. Of course, this wouldn’t leave you with much to use for calibration with modern temperature records.

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The only way to justify using the series in a regression model without a transformation to make it stationary…

One of the odd things about the time series that Steve is talking about (which exhibit d=0.50-\epsilon) is that they appear to correspond to stationary ARFIMA models — but just barely.

Why Mother Nature chooses to reside right there is a good question. I look to Koutsoyiannis…

]]>Hmmm! According to http://www.uoregon.edu/~robinh/gnmd03_basics.txt **linear regression** and **ANOVA** models are those which **assume** *independent and normally-distributed random variables with constant variance*. Maybe you’re thinking of **generalized linear models (GLMs)** that exist for regression-like modeling of data which do not assume a normal distribution.