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Water 2018, 10(6), 771; https://doi.org/10.3390/w10060771

A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise

1
Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 5, 15780 Zographou, Greece
2
Department of Civil and Environmental Engineering, University of California, Irvine 92697, CA, USA
*
Author to whom correspondence should be addressed.
Received: 26 April 2018 / Revised: 1 June 2018 / Accepted: 6 June 2018 / Published: 12 June 2018
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Abstract

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. View Full-Text
Keywords: Thomas-Fiering approach; linear stochastic models; autoregressive process; moving average; skewed white noise; bounded dependence patterns; synthetic data; simulation Thomas-Fiering approach; linear stochastic models; autoregressive process; moving average; skewed white noise; bounded dependence patterns; synthetic data; simulation
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Tsoukalas, I.; Papalexiou, S.M.; Efstratiadis, A.; Makropoulos, C. A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise. Water 2018, 10, 771.

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