Abstract
This study evaluates the joint impact of non-linearity and non-Gaussianity on predictive performance in 23 Brazilian monthly streamflow time series from 1931 to 2022. We consider point and interval forecasting, employing a PAR(p) model and comparing it with the periodic vine copula model. Results indicate that the Gaussian hypothesis assumed by PAR(p) is unsuitable; gamma and log-normal distributions prove more appropriate and crucial for constructing accurate confidence intervals. This is primarily due to the assumption of the Gaussian distribution, which can lead to the generation of confidence intervals with negative values. Analyzing the estimated copula models, we observed a prevalence of the bivariate Normal copula, indicating that linear dynamic dependence is frequent, and the Rotated Gumbel 180°, which exhibits lower tail dependence. Overall, the temporal dynamics are predominantly shaped by combining these two types of effects. In point forecasting, both models show similar behavior in the estimation set, with slight advantages for the copula model. The copula model performs better during the out-of-sample analysis, particularly for certain power plants. In interval forecasting, the copula model exhibits pronounced superiority, offering a better estimation of quantiles. Consistently demonstrating proficiency in constructing reliable and accurate intervals, the copula model reveals a notable advantage over the PAR(p) model in interval forecasting.
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Data availability
The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request. The time series were provided by the National System Operator (ONS) and are available at https://sintegre.ons.org.br.
Notes
A vine copula is a d-dimensional copula built from the combination of bivariate copulas. Because any bivariate copulas can be employed, vine copulas are renowned for their ability to model any dependency structure that can arise from a d-dimensional vector. For more details, see Aas et al. (2009).
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Conceptualization: [Guilherme Armando de Almeida Pereira, Álvaro de Lima Vega Filho]; Methodology: [Guilherme Armando de Almeida Pereira]; Formal analysis and investigation: [Guilherme Armando de Almeida Pereira], Writing: original draft preparation: [Guilherme Armando de Almeida Pereira, Álvaro de Lima Vega Filho]; Writing: review and editing: [Guilherme Armando de Almeida Pereira, Álvaro de Lima Vega Filho]; All authors read and approved the final manuscript.
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Appendix
Appendix
Figure 4
Table 9
Table 10
These are contour plots of the bivariate copula density functions employed in this research. Copulas can represent distinct types of dependence, such as asymmetry and tail dependence
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de Almeida Pereira, G.A., de Lima Veiga Filho, Á. Do non-linearity and non-Gaussianity truly matter in streamflow forecasting? A comparative study between PAR(p) and vine copula for Brazilian streamflow time series. Environ Monit Assess 196, 486 (2024). https://doi.org/10.1007/s10661-024-12645-8
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DOI: https://doi.org/10.1007/s10661-024-12645-8