This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct high-quality random functions, including those with non-fractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism -<F11.

Rescaled Range R=S analysis and Hurst Exponents are widely used as measures of long-term memory structures in stochastic processes. Our empirical studies show, however, that these statistics can incorrectly indicate departures from random walk behavior on short and intermediate time scales when very shortterm correlations are present. A modification of rescaled range estimation (R= ~ S analysis) intended to correct bias due to short-term dependencies was proposed by Lo (1991). We show, however, that Lo's R= ~ S statistic is itself biased and introduces other problems, including distortion of the Hurst exponents. We propose a new statistic R=S that corrects for mean bias in the range R, but does not suffer from the short term biases of R=S or Lo's R= ~ S. We support our conclusions with experiments on simulated random walk and AR(1) processes and experiments using high frequency interbank DEM / USD exchange rate quotes. We conclude that the DEM / USD series is mildly trending on t...

Standard flood return level estimation is based on extreme value analysis assuming independent extremes, i.e. fitting a model to excesses over a threshold or to annual maximum discharge. The assumption of independence might not be justifiable in many practical applications. The dependence of the daily run-off observations might in some cases be carried forward to the annual maximum discharge. Unfortunately, using the autocorrelation function, this effect is hard to detect in a short maxima series. One consequence of dependent annual maxima is an increasing uncertainty of the return level estimates, and is illustrated using a simulation study. The confidence intervals obtained from the asymptotic distribution of the Maximum-Likelihood estimator (MLE) for the generalized extreme value distribution (GEV) turned out to be too small to capture the resulting variability. In order to obtain more reliable confidence intervals, we compare four bootstrap strategies, out of which one yields promising results. The performance of this semi-parametric bootstrap strategy is studied in more detail. We exemplify this approach with a case study: a confidence limit for a 100-year return level estimate from a run-off series in southern Germany was calculated and compared to the result obtained using the asymptotic distribution of the MLE.