Martin Rypdal, Kristoffer Rypdal
The sunspot number (SSN), the total solar irradiance (TSI), a TSI
reconstruction, and the solar flare index (SFI), are analyzed for long-range
persistence (LRP). Standard Hurst analysis yields $H \approx 0.9$, which
suggests strong LRP. However, solar activity time series are non-stationary due
to the almost periodic 11 year smooth component, and the analysis does not give
the correct $H$ for the stochastic component. Better estimates are obtained by
detrended fluctuations analysis (DFA), but estimates are biased and errors are
large due to the short time records. These time series can be modeled as a
stochastic process of the form $x(t)=y(t)+\sigma \sqrt{y(t)}\, w_H(t)$, where
$y(t)$ is the smooth component, and $w_H(t) $ is a stationary fractional noise
with Hurst exponent $H$. From ensembles of numerical solutions to the
stochastic model, and application of Bayes' theorem, we can obtain bias and
error bars on $H$ and also a test of the hypothesis that a process is
uncorrelated ($H=1/2$). The conclusions from the present data sets are that
SSN, TSI and TSI reconstruction almost certainly are long-range persistent, but
with most probable value $H\approx 0.7$. The SFI process, however, is either
very weakly persistent ($H<0.6$) or completely uncorrelated. Some differences
between stochastic properties of the TSI and its reconstruction indicate some
error in the reconstruction scheme.
View original:
http://arxiv.org/abs/1111.4787
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