Testing hypotheses about sun-climate complexity linking.

We reexamine observational evidence presented in support of the hypothesis of a sun-climate complexity linking by N. Scafetta and B. J. West, Phys. Rev. Lett. 90, 248701 (2003)10.1103/PhysRevLett.90.248701, which contended that the integrated solar flare index (SFI) and the global temperature anomaly (GTA) both follow Lévy walk statistics with the same waiting-time exponent mu approximately 2.1. However, their analysis does not account for trends in the signal, cannot deal correctly with infinite variance processes (Lévy flights), and suffers from considering only the second moment. Our analysis shows that properly detrended, the integrated SFI is well described as a Lévy flight, and the integrated GTA as a persistent fractional Brownian motion. These very different stochastic properties of the solar and climate records do not support the hypothesis of a sun-climate complexity linking.