We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with …

sequence with memory. The memory effects are stronger the slower the perturbation. The adoption of a de-trending technique …

equities have no practical effect on the FX RV signatures. We show that local detrending of the high-frequency FX rate samples …

Determining trend and implementing detrending operations are important steps in data analysis. Yet there is neither … precise definition of “trend” nor any logical algorithm for extracting it. In this paper, we propose a Hybrid Detrending … detrending methods, our method is a posteriori, the trend defined by our method is only derived from the data. Further, our …

The rescaled range (R/S) analysis was used for analyzing the statistical persistence of air pollutants in Mexico City …-range persistence is not a uniform property over a wide range of time scales, from days to months. In fact, although the air pollutant … weekly) cycles are reflected in the dependence of the persistence strength as quantified in terms of the Hurst exponent. It …

geometry permits comparison with shell theory, as well as insight on dynamics of a virtual phase (as defined for persistence … than achieving the final stage of persistence. However, distinctive patterns of response can be identified for the …

conditions for extinction exponentially and persistence in the mean are established. The results are illustrated by computer …

number of consumers of the search engines has little contribution to their persistence, which is in agreement with the … persistence of the search engines and deduce new strategies. We also give suggestions for the web sites to cooperate with the …