Please follows the links: they include information on the persistence
phenomenon.
W. Eschenbach's sea level data for 63 stations with data from 1950 to 2015
with almost a completeness of 95%.
Data have been divided into 7 files (10 stations/file+3 stations).
Files named stat0n.txt with n=1,7
W. Eschenbach's post has been published at
https://wattsupwiththat.com/2017/07/20/sea-level-rise-accelerating-not/
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Data are autocorrelated, so the method by Koutsoyannis(2002) "The Hurst phenomenon and fractional Gaussian
noise made easy", Eq.(16) can be used. Its approximate formula, Eq.(17) is
r(k,j)=r(j)=H(2H-1)j^(2H-2) (17)
is useful to estimate H, Hurst exponent, given the lag-1 autocorrelation r(1).
r(1)=H(2H-1) ==> 2H^2-H-r=0 ==> H=[1+-sqrt(1+8r)]/4.
Autocorrelation reduces the number of indipendent data neff:
Nychka's formula is
neff=n[(1-r-0.68/sqrt(n))/(1+r+0.68/sqrt(n))]
where r=r(1)
Willis finds, in his first post on this subject, that
neff=n^(2-2H)
and Koutsoyannis confirms its correctness:
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" Demetris Koutsoyiannis July 1, 2015 at 2:04 pm
Willis, thank you very much for the excellent post and your
reference to my work. I confirm your result on the effective
sample size -see also equation (6) in
http://www.itia.ntua.gr/en/docinfo/781/ "
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.--.-.-.-.
Koutsoyannis,2006: In order to estimate H the standard deviation (Eq.3) of n
data samples can be computed and plotted (log-log scales) vs. n (ex:
n through
m/10, with m data number).An example il the fig.5 of the paper.
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FZ, August 9, 2017