Using Observed Functional Data to Simulate a Stochastic Process via a Random Multiplicative Cascade Model

2010 ◽  
pp. 453-460
Author(s):  
G. Damiana Costanzo ◽  
S. De Bartolo ◽  
F. Dell’Accio ◽  
G. Trombetta
Keyword(s):  
Stochastic Process ◽  
Functional Data ◽  
Cascade Model ◽  
Multiplicative Cascade

scholarly journals Towards Subdaily Rainfall Disaggregation via Clausius–Clapeyron

2014 ◽  
Vol 15 (3) ◽  
pp. 1303-1311 ◽  
Author(s):  
G. Bürger ◽  
M. Heistermann ◽  
A. Bronstert
Keyword(s):  
Temperature Dependence ◽  
Cascade Model ◽  
Proof Of Concept ◽  
Short Term ◽  
Temporal Disaggregation ◽  
Multiplicative Cascade

Abstract Two lines of research are combined in this study: first, the development of tools for the temporal disaggregation of precipitation, and second, some newer results on the exponential scaling of heavy short-term precipitation with temperature, roughly following the Clausius–Clapeyron (CC) relation. Having no extra temperature dependence, the traditional disaggregation schemes are shown to lack the crucial CC-type temperature dependence. The authors introduce a proof-of-concept adjustment of an existing disaggregation tool, the multiplicative cascade model of Olsson, and show that, in principal, it is possible to include temperature dependence in the disaggregation step, resulting in a fairly realistic temperature dependence of the CC type. They conclude by outlining the main calibration steps necessary to develop a full-fledged CC disaggregation scheme and discuss possible applications.

scholarly journals Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

2014 ◽  
Vol 21 (2) ◽  
pp. 477-487 ◽  
Author(s):  
Q. Cheng
Keyword(s):  
Fractal Dimension ◽  
Cascade Model ◽  
Nonlinear Properties ◽  
Cascade Processes ◽  
Insight Into ◽  
Multiplicative Cascade ◽  
Multifractal Modeling

Abstract. The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m1 of them receive d1 (> 0) and m2 receive d2 (> 0) proportion of the mass in the previous subset, respectively, where m1+m2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.

A Multiplicative Cascade Model for High-Resolution Space-Time Downscaling of Rainfall

2018 ◽  
Vol 123 (4) ◽  
pp. 2050-2067 ◽  
Author(s):  
Bhupendra A. Raut ◽  
Alan W. Seed ◽  
Michael J. Reeder ◽  
Christian Jakob
Keyword(s):  
High Resolution ◽  
Space Time ◽  
Cascade Model ◽  
Multiplicative Cascade

scholarly journals A STOCHASTIC CASCADE MODEL FOR FX DYNAMICS

2000 ◽  
Vol 03 (03) ◽  
pp. 357-360 ◽  
Author(s):  
WOLFGANG BREYMANN ◽  
SHOALEH GHASHGHAIE ◽  
PETER TALKNER
Keyword(s):  
Information Flow ◽  
Cascade Model ◽  
Time Interval ◽  
Hydrodynamic Turbulence ◽  
Time Horizons ◽  
Structural Peculiarities ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed ◽  
Short Time ◽  
Multiplicative Cascade

A time series model for the FX dynamics is presented which takes into account structural peculiarities of the market, namely its heterogeneity and an information flow from long to short time horizons. The model emerges from an analogy between FX dynamics and hydrodynamic turbulence. The heterogeneity of the market is modeled in the form of a multiplicative cascade of time scales ranging from several minutes to a few months, analogous to the Kolmogorov cascade in turbulence. The model reproduces well the important empirical characteristics of FX rates for major currencies, as the heavy-tailed distribution of returns, their change in shape with the increasing time interval, and the persistence of volatility.

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