相关系数准则对水文相依模型的适用性及验证

相依变异是水文过程变异的一种重要表征形式，可以用自回归、滑动平均和自回归滑动平均模型进行描述，但如何有效地确定模型阶数是前提和关键。相关系数准则是针对自回归模型提出的定阶准则，该准则基于相依成分与原序列间的相关系数指标，计算其均方误差以反映模型的拟合优劣，并构造信息熵函数以衡量模型不确定性及复杂程度。本文基于相关系数定阶准则，尝试探讨该准则对于滑动平均和自回归滑动平均模型的适用性。以三阶以内的滑动平均模型和自回归滑动平均模型为例，统计试验表明：相关系数准则所判定阶数相较于其它两种常用的准则更为准确。最后选取实测水文序列对其进行验证，结果表明该定阶准则同样适用于滑动平均和自回归滑动平均模型。

Applicability of correlation coefficient information criterion to hydrological dependence models and its validation

Dependence variation, an important feature of hydrological variation, can be described using autoregressive (AR(p)), moving average (MA(q)), and autoregressive moving average (ARMA(p, q)) models with p and q standing for the orders of autoregression and moving average, respectively. However, application and accuracy of these models depend on effective determination of their orders. Correlation coefficient information criterion (RIC) is adopted in previous studies to determine the order of an AR(p) model, where its fitting is assessed by the mean square error and its complexity is quantified based on information entropy. This study examines the applicability of RIC criterion to MA(q) and ARMA(p, q) and evaluate its performance. For the MA(q) models (q ≤ 3) and ARMA(p, q) models (p+q ≤ 3), our statistical experiments show its accuracy is much higher than those of the BIC and AIC criteria in determining the model orders. We demonstrate it is applicable to MA(q) and ARMA(p, q) in terms of multiple observed hydrological series.