@misc{Koechy2006,
  author    = {K{\"o}chy, Martin},
  title     = {Stochastic time series of daily precipitation for the interior of Israel},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-13155},
  year      = {2006},
  abstract  = {This contribution describes a generator of stochastic time series of daily precipitation for the interior of Israel from c. 90 to 900 mm mean annual precipitation (MAP) as a tool for studies of daily rain variability. The probability of rainfall on a given day of the year is described by a regular Gaussian peak curve function. The amount of rain is drawn randomly from an exponential distribution whose mean is the daily mean rain amount (averaged across years for each day of the year) described by a flattened Gaussian peak curve. Parameters for the curves have been calculated from monthly aggregated, long-term rain records from seven meteorological stations. Parameters for arbitrary points on the MAP gradient are calculated from a regression equation with MAP as the only independent variable. The simple structure of the generator allows it to produce time series with daily rain patterns that are projected under climate change scenarios and simultaneously control MAP. Increasing within-year variability of daily precipitation amounts also increases among-year variability of MAP as predicted by global circulation models. Thus, the time series incorporate important characteristics for climate change research and represent a flexible tool for simulations of daily vegetation or surface hydrology dynamics.},
  language  = {en}
}
@misc{ŚlęzakMetzlerMagdziarz2019,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Codifference can detect ergodicity breaking and non-Gaussianity},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {748},
  doi       = {10.25932/publishup-43617},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436178},
  pages     = {25},
  year      = {2019},
  abstract  = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.},
  language  = {en}
}
@article{ŚlęzakMetzlerMagdziarz2019,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Codifference can detect ergodicity breaking and non-Gaussianity},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab13f3},
  pages     = {25},
  year      = {2019},
  abstract  = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.},
  language  = {en}
}