Nicola Scafetta has demonstrated that Diffusion Entropic Analysis can identify physical phenomena underlying complex time series, including non-Gaussian Levy and other series. This appears an important development in detecting complex physical phenomena resulting in time series measurements.
Scafetta’s work promises to be important in detecting and distinguishing Complex Specified Information from natural complex phenomena. e.g. for Jill Tarter of SETI to detect and distinguish extra terrestrial communications from complex natural phenomena.
The power of this method is shown in Scafetta’s application of this DEA method to detecting complex correlations between solar activity and earth’s climate. See: Nicola Scafetta and Bruce J. West, “Is climate sensitive to solar variability?” Physics Today, 3 50-51 (2008).
See also his 2009 EPA presentation: “Climate Change and Its causes: A Discussion about Some Key Issues” N. Scafetta. Invited author at the U. S. Environmental Protection Agency, DC USA, February 26, 2009.
Scafetta’s Presentation Slides
From the sun’s rotation around the solar system’s center of mass, Scafetta has developed a model that appears to identify the solar signature in climate. See Slide 66 of his Presentation slides.
This explains the 1910-1945 warming and implies that about 70% of the observed warming from 1975 to 2002 was part of this natural climate cycle during its warm phase.
There is also a very interesting 60 year correlation between this motion of the Sun and the Earth’s “Length Of Day”. See Scafetta’s Slide 67, and Mazzarella, Solar Forcing of Changes in Atmospheric Circulation and Earth’s Rotation and Climate”, The Open Atmospheric Science Journal 2008, 2, 181-184
For those concerned that anthropogenic CO2 is not receiving its justified weighting, Douglass and Christy have examined recent temperature trends to distinguish the expected linear CO2 signature from other phenomena. See: Limits on CO2 Climate Forcing from Recent Temperature Data of Earth” David H. Douglass, John R. Christy Energy & Environment, Volume 20, Numbers 1-2, January 2009 , pp. 177-189(13).
“The trend expected from CO2 climate forcing is 0.070g ºC/decade, where g is the gain due to any feedback. If the underlying trend is due to CO2 then g~1. Models giving values of g greater than 1 would need a negative climate forcing to partially cancel that from CO2. This negative forcing cannot be from aerosols.”
(PS The expected CO2 signature is linear as being the log of an exponentially increasing concentration.)
Nicola Scafetta, Dissertation: An entropic approach to the analysis of time series.
Statistical analysis of time series. With compelling arguments we show that the Diffusion Entropy Analysis (DEA) is the only method of the literature of the Science of Complexity that correctly determines the scaling hidden within a time series reflecting a Complex Process.
The time series is thought of as a source of fluctuations, and the DEA is based on the Shannon entropy of the diffusion process generated by these fluctuations. All traditional methods of scaling analysis, instead, are based on the variance of this diffusion process. The variance methods detect the real scaling only if the Gaussian assumption holds true. We call H the scaling exponent detected by the variance methods and d the real scaling exponent. If the time series is characterized by Fractional Brownian Motion, we have H¹d and the scaling can be safely determined, in this case, by using the variance methods. If, on the contrary, the time series is characterized, for example, by Lévy statistics, H ¹ d and the variance methods cannot be used to detect the true scaling. Lévy walk yields the relation d=1/(3-2H). In the case of Lévy flights, the variance diverges and the exponent H cannot be determined, whereas the scaling d exists and can be established by using the DEA. Therefore, only the joint use of two different scaling analysis methods, the variance scaling analysis and the DEA, can assess the real nature, Gauss or Lévy or something else, of a time series. Moreover, the DEA determines the information content, under the form of Shannon entropy, or of any other convenient entopic indicator, at each time step of the process that, given a sufficiently large number of data, is expected to become diffusion with scaling. This makes it possible to study the regime of transition from dynamics to thermodynamics, non-stationary regimes, and the saturation regime as well.
First of all, the efficiency of the DEA is proved with theoretical arguments and with numerical work on artificial sequences. Then we apply the DEA to three different sets of real data, Genome sequences, hard x-ray solar flare waiting times and sequences of sociological interest. In all these cases the DEA makes new properties, overlooked by the standard method of analysis, emerge.
University of North Texas, 2001.
3 Replies to “Diffusion Entropic Analysis to model natural complex time series vs CSI”
I read more research by Scaffetta from your links.
Not sure if you read this paper:
Le´vy scaling: The diffusion entropy analysis applied to DNA sequences
Scafetta finding Levy sequence statistics in DNA rather than Gaussian is interesting.
I’m sure it is. English translation, anyone? What is the significance of Gaussian vs. Levy sequence statistics?