Applications of statistical physics to economic and financial topics

TLDR: In this article, the existence or not of long-, medium-, short-range power-law correlations in economic systems as well as to the presence of financial cycles are investigated, and the possibility of crash predictions is indicated.

Abstract: Problems in economy and finance have started to attract the interest of statistical physicists. Fundamental problems pertain to the existence or not of long-, medium-, short-range power-law correlations in economic systems as well as to the presence of financial cycles. Methods like the extended detrended fluctuation analysis, and the multi-affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability. Among spectacular results, the possibility of crash predictions is indicated. The well known financial analyst technique, the so-called moving average, is shown to raise questions about fractional Brownian motion properties. Finally, the (m,k)-Zipf method and the i-variability diagram technique are presented for sorting out short range correlations. Analogies with other fields of modern applied statistical physics are also presented in view of some universal openess.