Water Resources Research Center (SUARGE), Adnan Menderes University, 09100, Aydin, Turkey.
Environ Monit Assess. 2010 Oct;169(1-4):687-701. doi: 10.1007/s10661-009-1208-y. Epub 2009 Oct 21.
In the present study, a seasonal and non-seasonal prediction of boron concentrations time series data for the period of 1996-2004 from Büyük Menderes river in western Turkey are addressed by means of linear stochastic models. The methodology presented here is to develop adequate linear stochastic models known as autoregressive integrated moving average (ARIMA) and multiplicative seasonal autoregressive integrated moving average (SARIMA) to predict boron content in the Büyük Menderes catchment. Initially, the Box-Whisker plots and Kendall's tau test are used to identify the trends during the study period. The measurements locations do not show significant overall trend in boron concentrations, though marginal increasing and decreasing trends are observed for certain periods at some locations. ARIMA modeling approach involves the following three steps: model identification, parameter estimation, and diagnostic checking. In the model identification step, considering the autocorrelation function (ACF) and partial autocorrelation function (PACF) results of boron data series, different ARIMA models are identified. The model gives the minimum Akaike information criterion (AIC) is selected as the best-fit model. The parameter estimation step indicates that the estimated model parameters are significantly different from zero. The diagnostic check step is applied to the residuals of the selected ARIMA models and the results indicate that the residuals are independent, normally distributed, and homoscadastic. For the model validation purposes, the predicted results using the best ARIMA models are compared to the observed data. The predicted data show reasonably good agreement with the actual data. The comparison of the mean and variance of 3-year (2002-2004) observed data vs predicted data from the selected best models show that the boron model from ARIMA modeling approaches could be used in a safe manner since the predicted values from these models preserve the basic statistics of observed data in terms of mean. The ARIMA modeling approach is recommended for predicting boron concentration series of a river.
在本研究中，通过线性随机模型对来自土耳其西部大曼德雷斯河的硼浓度时间序列数据进行了季节性和非季节性预测，研究时间为 1996 年至 2004 年。这里提出的方法是开发适当的线性随机模型，称为自回归综合移动平均（ARIMA）和乘法季节性自回归综合移动平均（SARIMA），以预测大曼德雷斯流域的硼含量。最初，使用箱线图和 Kendall 的 tau 检验来识别研究期间的趋势。测量地点的硼浓度没有显示出显著的整体趋势，尽管在某些地点的某些时期观察到了边际增加和减少的趋势。ARIMA 建模方法包括以下三个步骤：模型识别、参数估计和诊断检查。在模型识别步骤中，考虑到硼数据序列的自相关函数（ACF）和偏自相关函数（PACF）结果，确定了不同的 ARIMA 模型。选择最小 Akaike 信息准则（AIC）的模型作为最佳拟合模型。参数估计步骤表明，估计的模型参数与零显著不同。诊断检查步骤应用于所选 ARIMA 模型的残差，结果表明残差是独立的、正态分布的和同方差的。为了验证模型，将最佳 ARIMA 模型的预测结果与观测数据进行了比较。预测数据与实际数据相当吻合。将所选最佳模型的 3 年（2002-2004 年）观测数据的均值和方差与预测数据进行比较表明，ARIMA 建模方法的硼模型可以安全使用，因为这些模型的预测值保留了观测数据的基本统计数据，即均值。建议使用 ARIMA 建模方法来预测河流的硼浓度序列。
