Armanini Stefanan Aline, Sagrillo Murilo, Palm Bruna G, Bayer Fábio M
Postgraduate Program in Industrial Engineering, Universidade Federal de Santa Maria, Santa Maria, Rio Grande do Sul, Brazil.
Department of Mathematics and Natural Sciences, Blekinge Institute of Technology, Karlskrona, Blekinge, Sweden.
PLoS One. 2025 May 20;20(5):e0324721. doi: 10.1371/journal.pone.0324721. eCollection 2025.
This paper proposes the MKSARMAX model for modeling and forecasting time series that can only take on values within a specified range, such as in the interval (0,1). The model is especially good for modeling double-bounded hydro-environmental time series since it accommodates bounded support and asymmetric distribution, making it advantageous compared to the traditional Gaussian-based time series model. The MKSARMAX models the conditional median of a modified Kumaraswamy distributed variable observed over time, by a dynamic structure considering stochastic seasonality and including autoregressive and moving average terms, exogenous regressors, and a link function. The conditional maximum likelihood method is employed to estimate the model parameters. Hypothesis tests and confidence intervals for the parameters of the proposed model are derived using the asymptotic theory of the conditional maximum likelihood estimators. Quantile residuals are defined for diagnostic analysis, and goodness-of-fit tests are subsequently implemented. Synthetic hydro-environmental time series are generated in a Monte Carlo simulation study to assess the finite sample performance of the inferences. Moreover, MKSARMAX outperforms βSARMA, SARMAX, Holt-Winters, and KARMA models in most accuracy measures analyzed when applied to useful water volume datasets, presenting for the first-step forecast at least [Formula: see text] lower MAE, RMSE, and MAPE values than competitors in the Caconde UV dataset, and [Formula: see text] lower MAE, RMSE, and MAPE values than competitors in the Guarapiranga UV dataset. These findings suggest that the MKSARMAX model holds strong potential for water resource management. Its flexibility and accuracy in the early forecasting steps make it particularly valuable for predicting flood and drought periods.
本文提出了MKSARMAX模型，用于对只能在指定范围内取值的时间序列进行建模和预测，例如在区间(0,1)内。该模型特别适用于对双边界水文环境时间序列进行建模，因为它考虑了有界支持和非对称分布，与传统的基于高斯的时间序列模型相比具有优势。MKSARMAX通过考虑随机季节性的动态结构对随时间观测的修正Kumaraswamy分布变量的条件中位数进行建模，该结构包括自回归和移动平均项、外生回归变量以及一个链接函数。采用条件最大似然法估计模型参数。利用条件最大似然估计量的渐近理论推导了所提出模型参数的假设检验和置信区间。定义了分位数残差用于诊断分析，随后进行了拟合优度检验。在蒙特卡罗模拟研究中生成了合成水文环境时间序列，以评估推断的有限样本性能。此外，当应用于有用水量数据集时，在分析的大多数准确性指标中，MKSARMAX的表现优于βSARMA、SARMAX、Holt-Winters和KARMA模型，在Caconde紫外线数据集的第一步预测中，其平均绝对误差（MAE）、均方根误差（RMSE）和平均绝对百分比误差（MAPE）值比竞争对手至少低[公式：见原文]，在Guarapiranga紫外线数据集的第一步预测中，其MAE、RMSE和MAPE值比竞争对手至少低[公式：见原文]。这些发现表明，MKSARMAX模型在水资源管理方面具有很大的潜力。它在早期预测步骤中的灵活性和准确性使其在预测洪水和干旱时期特别有价值。
