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Using detrended fluctuation analysis (DFA), we study long-term correlations in wind speed data. We find that not only the wind speed data themselves but also their volatilities possess long-range correlations, expressed by the fluctuation exponent α being larger than one half. We also perform a multifractal analysis. Whereas most data sets show a broad multifractal spectrum, recordings of two days, obtained at the same measurement site, are essentially monofractal. By surrogate analysis, we confirm the monofractal nature of these data. Our analysis shows that correlated volatility does not necessarily imply multifractality (as often assumed) and that a given system may exhibit both mono- and multifractal signals, depending on system parameters.

We present a simple method to estimate probability currents of stochastic systems from a given time series. The method uses results of the theory of stochastic differential equations about conditional averages. Evaluation of the probability current directly aims at detecting the violation of detailed balance and hence yields the proper characterisation of nonequilibrium behaviour. We apply our approach to stochastic resonance and propose a novel resonance criterion which is based on the evaluation of the probability current. It agrees well with other measures, e.g. derived from correlations or signal-to-noise ratios. Finally, we demonstrate on an example of experimental wind data that our approach copes with real experimental data sets as well.

We present a new approach, based on a locally low-dimensional prediction scheme, which was originally developed for deterministic chaotic signals, to detect the deterministic structure of local surface wind velocities. By exploiting properties of the signal which mimic the deterministic structure created by non-linear coherent effects of a turbulent fluid and by resolving the strong inherent non-stationarity as a sequence of different dynamical regimes, short time predictions of future wind velocities can be performed. Although on average no reduction of the prediction error can be achieved using a non-linear model instead of a linear stochastic one, intermittent gusts can be predicted with significantly higher accuracy. An asymmetry in the predictability is observed, which suggests that an increase of the velocity is rather deterministic, whereas the subsequent decrease is dominated by a stochastic behaviour.

Times series obtained from dynamical systems can be converted into sequences of time intervals between relevant events. We show that under quite general conditions time intervals are phase space observables and therefore embedding theorems for the reconstruction of a state space from scalar signals are valid. The practical applicability in data analysis is discussed with the help of numerical and experimental examples.

We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding to regular islands of the uncoupled maps. As a consequence, we observe long intermediate regimes of power-law decay of the recurrence time statistics (with exponent $\gamma=0.5$) and of ballistic motion. The asymptotic decay of correlations and anomalous diffusion depend on the stickiness of the $N$-dimensional invariant tori. Detailed numerical simulations show weaker stickiness for increasing $N$ suggesting that high-dimensional Hamiltonian systems asymptotically fulfill the demands of the usual hypotheses of strong chaos., Comment: 5 pages, 3 figures. Revised version with small changes