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A cautionary note on the reproduction of dependencies through linear stochastic models with non-Gaussian white noise
Publikationstyp
Journal Article
Date Issued
2018-06-12
Sprache
English
Author(s)
Journal
Volume
10
Issue
6
Article Number
771
Citation
Water 10 (6): 771 (2018)
Publisher DOI
Scopus ID
Publisher
MDPI
Since the prime days of stochastic hydrology back in 1960s, autoregressive (AR) and moving average (MA) models (as well as their extensions) have been widely used to simulate hydrometeorological processes. Initially, AR(1) or Markovian models with Gaussian noise prevailed due to their conceptual and mathematical simplicity. However, the ubiquitous skewed behavior of most hydrometeorological processes, particularly at fine time scales, necessitated the generation of synthetic time series to also reproduce higher-order moments. In this respect, the former schemes were enhanced to preserve skewness through the use of non-Gaussian white noise- a modification attributed to Thomas and Fiering (TF). Although preserving higher-order moments to approximate a distribution is a limited and potentially risky solution, the TF approach has become a common choice in operational practice. In this study, almost half a century after its introduction, we reveal an important flaw that spans over all popular linear stochastic models that employ non-Gaussian white noise. Focusing on the Markovian case, we prove mathematically that this generating scheme provides bounded dependence patterns, which are both unrealistic and inconsistent with the observed data. This so-called "envelope behavior" is amplified as the skewness and correlation increases, as demonstrated on the basis of real-world and hypothetical simulation examples.
Subjects
Autoregressive process
Bounded dependence patterns
Linear stochastic models
Moving average
Simulation
Skewed white noise
Synthetic data
Thomas-Fiering approach
DDC Class
551: Geology, Hydrology Meteorology