I. Tsoukalas, S.M. Papalexiou, A. Efstratiadis, and C. Makropoulos, A cautionary note on the reproduction of dependencies through linear stochastic models with non-Gaussian white noise, *Water*, 10 (6), 771, doi:10.3390/w10060771, 2018.

[doc_id=1848]

[English]

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.

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**See also:**
http://www.mdpi.com/2073-4441/10/6/771

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**Our works that reference this work:**

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3. | I. Tsoukalas, A. Efstratiadis, and C. Makropoulos, Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation structure, Journal of Hydrology, 575, 354–380, doi:10.1016/j.jhydrol.2019.05.017, 2019. |

4. | P. Kossieris, I. Tsoukalas, C. Makropoulos, and D. Savic, Simulating marginal and dependence behaviour of water demand processes at any fine time scale, Water, 11 (5), 885, doi:10.3390/w11050885, 2019. |

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**Other works that reference this work (this list might be obsolete):**

1. | Papalexiou, S. M., Y. Markonis, F. Lombardo, A. AghaKouchak, and E. Foufoula‐Georgiou, Precise temporal Disaggregation Preserving Marginals and Correlations (DiPMaC) for stationary and non‐stationary processes, Water Resources Research, doi:10.1029/2018WR022726, 2018. |

2. | Cheng, Y., P. Feng, J. Li, Y. Guo, and P. Ren, Water supply risk analysis based on runoff sequence simulation with change point under changing environment, Advances in Meteorology, 9619254, doi:10.1155/2019/9619254, 2019. |

3. | Marković, D., S. Ilić, D. Pavlović, J. Plavšić, and N. Ilich, Multivariate and multi-scale generator based on non-parametric stochastic algorithms, Journal of Hydroinformatics, jh2019071, doi:10.2166/hydro.2019.071, 2019. |

4. | Nazemi, A., M. Zaerpour, and E. Hassanzadeh, Uncertainty in bottom-up vulnerability assessments of water supply systems due to regional streamflow generation under changing conditions, Journal of Water Resources Planning and Management, 146(2), doi:10.1061/(ASCE)WR.1943-5452.0001149, 2020. |

**Tagged under:**
Stochastics