Water Resources Management

, Volume 33, Issue 10, pp 3417–3431 | Cite as

Periodic Copula Autoregressive Model Designed to Multivariate Streamflow Time Series Modelling

  • Guilherme Armando de Almeida PereiraEmail author
  • Álvaro Veiga


It is a challenge to develop models that can represent the stochastic behaviour of rivers and basins. Currently used streamflow models were constructed under rigid hypotheses. Hence, these models are limited in their ability to represent nonlinear dependencies and/or unusual distributions. Copulas help overcome these limitations and are being employed widely for modelling hydrological data. For instance, pure copula-based models have been proposed to simulate univariate hydrological series. However, there have been few studies on the use of copulas to model multivariate inflow series. Thus, the aim of this study is to develop a pure copula-based model for simulating periodic multivariate streamflow scenarios, wherein temporal and spatial dependencies are considered. The model was employed in a set of 11 affluent natural energy series from Brazil. We used the model to simulate many scenarios and analyze them through statistical tests such as Levene’s test, the Kolmogorov-Smirnov test, Kupiec test, and t-test. In addition, we investigated the spatial and temporal dependence of the scenarios. Finally, the critical periods of the simulated scenarios were investigated. The results indicated that the proposed model is capable of simulating scenarios that preserve historical features observed in the original data.


Non-linear models Stochastic streamflow simulation Copula models for multivariate streamflow time series Periodic multivariate copula model 



The authors would like to thank the National Council for Scientific and Technological Development (CNPq) of Brazil for support through the CNPq-PDJ program (grant number 150866/2017-8).

Compliance with Ethical Standards

Conflict of interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Economics - Econometrics Research GroupFederal University of Espírito SantoVitoriaBrazil
  2. 2.Department of Electrical EngineeringPontifical Catholic University of Rio de JaneiroGáveaBrazil

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