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Author: Rust, H.W. × Version: publishedVersion ×

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    Statistical characteristics of surrogate data based on geophysical measurements
    (Göttingen : Copernicus, 2006) Venema, V.; Bachner, S.; Rust, H.W.; Simmer, C.
    In this study, the statistical properties of a range of measurements are compared with those of their surrogate time series. Seven different records are studied, amongst others, historical time series of mean daily temperature, daily rain sums and runoff from two rivers, and cloud measurements. Seven different algorithms are used to generate the surrogate time series. The best-known method is the iterative amplitude adjusted Fourier transform (IAAFT) algorithm, which is able to reproduce the measured distribution as well as the power spectrum. Using this setup, the measurements and their surrogates are compared with respect to their power spectrum, increment distribution, structure functions, annual percentiles and return values. It is found that the surrogates that reproduce the power spectrum and the distribution of the measurements are able to closely match the increment distributions and the structure functions of the measurements, but this often does not hold for surrogates that only mimic the power spectrum of the measurement. However, even the best performing surrogates do not have asymmetric increment distributions, i.e., they cannot reproduce nonlinear dynamical processes that are asymmetric in time. Furthermore, we have found deviations of the structure functions on small scales.
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    Tempting long-memory - on the interpretation of DFA results
    (Göttingen : Copernicus GmbH, 2004) Maraun, D.; Rust, H.W.; Timmer, J.
    We study the inference of long-range correlations by means of Detrended Fluctuation Analysis (DFA) and argue that power-law scaling of the fluctuation function and thus long-memory may not be assumed a priori but have to be established. This requires the investigation of the local slopes. We account for the variability characteristic for stochastic processes by calculating empirical confidence regions. Comparing a long-memory with a short-memory model shows that the inference of long-range correlations from a finite amount of data by means of DFA is not specific. We remark that scaling cannot be concluded from a straight line fit to the fluctuation function in a log-log representation. Furthermore, we show that a local slope larger than α=0.5 for large scales does not necessarily imply long-memory. We also demonstrate, that it is not valid to conclude from a finite scaling region of the fluctuation function to an equivalent scaling region of the autocorrelation function. Finally, we review DFA results for the Prague temperature data set and show that long-range correlations cannot not be concluded unambiguously.
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    Trend assessment: Applications for hydrology and climate research
    (Göttingen : Copernicus GmbH, 2005) Kallache, M.; Rust, H.W.; Kropp, J.
    The assessment of trends in climatology and hydrology still is a matter of debate. Capturing typical properties of time series, like trends, is highly relevant for the discussion of potential impacts of global warming or flood occurrences. It provides indicators for the separation of anthropogenic signals and natural forcing factors by distinguishing between deterministic trends and stochastic variability. In this contribution river run-off data from gauges in Southern Germany are analysed regarding their trend behaviour by combining a deterministic trend component and a stochastic model part in a semi-parametric approach. In this way the trade-off between trend and autocorrelation structure can be considered explicitly. A test for a significant trend is introduced via three steps: First, a stochastic fractional ARIMA model, which is able to reproduce short-term as well as long-term correlations, is fitted to the empirical data. In a second step, wavelet analysis is used to separate the variability of small and large time-scales assuming that the trend component is part of the latter. Finally, a comparison of the overall variability to that restricted to small scales results in a test for a trend. The extraction of the large-scale behaviour by wavelet analysis provides a clue concerning the shape of the trend.