@phdthesis{Rust2007,
  author    = {Rust, Henning},
  title     = {Detection of long-range dependence : applications in climatology and hydrology},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13347},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {It is desirable to reduce the potential threats that result from the variability of nature, such as droughts or heat waves that lead to food shortage, or the other extreme, floods that lead to severe damage. To prevent such catastrophic events, it is necessary to understand, and to be capable of characterising, nature's variability. Typically one aims to describe the underlying dynamics of geophysical records with differential equations. There are, however, situations where this does not support the objectives, or is not feasible, e.g., when little is known about the system, or it is too complex for the model parameters to be identified. In such situations it is beneficial to regard certain influences as random, and describe them with stochastic processes. In this thesis I focus on such a description with linear stochastic processes of the FARIMA type and concentrate on the detection of long-range dependence. Long-range dependent processes show an algebraic (i.e. slow) decay of the autocorrelation function. Detection of the latter is important with respect to, e.g. trend tests and uncertainty analysis. Aiming to provide a reliable and powerful strategy for the detection of long-range dependence, I suggest a way of addressing the problem which is somewhat different from standard approaches. Commonly used methods are based either on investigating the asymptotic behaviour (e.g., log-periodogram regression), or on finding a suitable potentially long-range dependent model (e.g., FARIMA[p,d,q]) and test the fractional difference parameter d for compatibility with zero. Here, I suggest to rephrase the problem as a model selection task, i.e.comparing the most suitable long-range dependent and the most suitable short-range dependent model. Approaching the task this way requires a) a suitable class of long-range and short-range dependent models along with suitable means for parameter estimation and b) a reliable model selection strategy, capable of discriminating also non-nested models. With the flexible FARIMA model class together with the Whittle estimator the first requirement is fulfilled. Standard model selection strategies, e.g., the likelihood-ratio test, is for a comparison of non-nested models frequently not powerful enough. Thus, I suggest to extend this strategy with a simulation based model selection approach suitable for such a direct comparison. The approach follows the procedure of a statistical test, with the likelihood-ratio as the test statistic. Its distribution is obtained via simulations using the two models under consideration. For two simple models and different parameter values, I investigate the reliability of p-value and power estimates obtained from the simulated distributions. The result turned out to be dependent on the model parameters. However, in many cases the estimates allow an adequate model selection to be established. An important feature of this approach is that it immediately reveals the ability or inability to discriminate between the two models under consideration. Two applications, a trend detection problem in temperature records and an uncertainty analysis for flood return level estimation, accentuate the importance of having reliable methods at hand for the detection of long-range dependence. In the case of trend detection, falsely concluding long-range dependence implies an underestimation of a trend and possibly leads to a delay of measures needed to take in order to counteract the trend. Ignoring long-range dependence, although present, leads to an underestimation of confidence intervals and thus to an unjustified belief in safety, as it is the case for the return level uncertainty analysis. A reliable detection of long-range dependence is thus highly relevant in practical applications. Examples related to extreme value analysis are not limited to hydrological applications. The increased uncertainty of return level estimates is a potentially problem for all records from autocorrelated processes, an interesting examples in this respect is the assessment of the maximum strength of wind gusts, which is important for designing wind turbines. The detection of long-range dependence is also a relevant problem in the exploration of financial market volatility. With rephrasing the detection problem as a model selection task and suggesting refined methods for model comparison, this thesis contributes to the discussion on and development of methods for the detection of long-range dependence.},
  language  = {en}
}
@article{MaraunRustOsborn2009,
  author    = {Maraun, Douglas and Rust, Henning W. and Osborn, Tim J.},
  title     = {The annual cycle of heavy precipitation across the United Kingdom : a model based on extreme value statistics},
  issn      = {0899-8418},
  doi       = {10.1002/Joc.1811},
  year      = {2009},
  abstract  = {The annual cycle of extreme I-day precipitation events across the UK is investigated by developing a statistical model and fitting it to data from 689 rain gauges A generalized extrerne-value distribution (GEV) is fit to the time series of monthly maxima, across all months of the year simultaneously, by approximating, the annual cycles of the location and scale parameters by harmonic functions, while keeping the shape parameter constant throughout the year We average the shape parameter of neighbouring rain gauges to decrease uncertainties. and also Interpolate values of all model parameters to give complete coverage of (lie UK. The model reveals distinct spatial patterns the estimated parameters The annual mean of the location and scale parameter is highly correlated with orography. The annual cycle of the location parameter is strong in the northwest UK (peaking in late autumn or winter) and in East Anglia (where it peaks HI late summer), and low in the Midlands The annual cycle of the scale parameter exhibits a similar pattern with strongest amplitudes in East Anglia The spatial patterns of the annual cycle phase suggest that they are linked to the dominance of frontal precipitation for generating extreme precipitation in the west and convective precipitation in the southeast of the UK The shape parameter shows a gradient from Positive Values in the east to negative values in some areas of the west We also estimate 10-year and 100-year return levels at each rain gauge, and interpolated across the UK.},
  language  = {en}
}