水文序列相依变异识别的RIC定阶准则——以自回归模型为例
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摘要
水文过程相依性是水文变异的主要表现形式之一,应用自回归模型对其进行拟合时合理确定模型阶数是一个难点问题。本文在分析AIC和BIC准则的基础上,提出了一种以原序列与其相依成分的相关系数作为拟合度指标,同时借用信息熵形式的函数式,作为模型不确定性度量指标的自回归模型定阶准则(简称RIC准则)。以AR(1)、AR(2)、AR(3)和AR(4)模型为例进行统计试验,将不同序列长度下该准则的定阶准确率与其他定阶准则进行比较,试验结果表明,RIC准则对于上述模型均具有较好的适应性,且定阶准确率远高于AIC准则,其中对于前三阶模型RIC准则优于BIC准则,但四阶模型略低于BIC准则。RIC准则的优势是可以同时满足模型定阶、相依程度分级与模型检验的需求,将其应用于实测水文序列分析,结果显示,该准则能较准确地识别自回归模型的阶数,且符合提出的"相依有变异而残差无变异的最小阶数"的检验标准。
The dependence of hydrological processes is one of the main manifestations of hydrological variability. It is a difficult problem to determine the model order reasonably when using autoregressive model to fit it. Based on the analysis of AIC and BIC criteria,this paper proposed an autoregressive model's order determination criterion referred to as RIC,which takes the correlation coefficient between the original series and its dependent components as the fitting index and takes the function formula in the form of information entropy as the measurement index of model uncertainty. Taking AR(1),AR(2),AR(3) and AR(4) models as examples for statistical experiments,and the accuracy of this criterion was compared with other order determined criteria in different sequence lengths. The results show that RIC has good adaptability to the above models and the accuracy of order determination is much higher than AIC. For the first three-order model,RIC performs better than BIC,but is slightly lower than BIC for the fourth-order model. The advantage of the RIC criterion is that it can simultaneously satisfy the requirements of model ordering,dependency degree grading and model checking. Applying it to the analysis of measured hydrological sequence,the results show that the criterion could accurately identify the order of the autoregressive model and conform to the proposed test standard of"minimum order with variation in dependent parts and no variation in residuals".
The dependence of hydrological processes is one of the main manifestations of hydrological variability. It is a difficult problem to determine the model order reasonably when using autoregressive model to fit it. Based on the analysis of AIC and BIC criteria,this paper proposed an autoregressive model's order determination criterion referred to as RIC,which takes the correlation coefficient between the original series and its dependent components as the fitting index and takes the function formula in the form of information entropy as the measurement index of model uncertainty. Taking AR(1),AR(2),AR(3) and AR(4) models as examples for statistical experiments,and the accuracy of this criterion was compared with other order determined criteria in different sequence lengths. The results show that RIC has good adaptability to the above models and the accuracy of order determination is much higher than AIC. For the first three-order model,RIC performs better than BIC,but is slightly lower than BIC for the fourth-order model. The advantage of the RIC criterion is that it can simultaneously satisfy the requirements of model ordering,dependency degree grading and model checking. Applying it to the analysis of measured hydrological sequence,the results show that the criterion could accurately identify the order of the autoregressive model and conform to the proposed test standard of"minimum order with variation in dependent parts and no variation in residuals".
引文
[1]鲁帆,肖伟华,严登华,等.非平稳时间序列极值统计模型及其在气候-水文变化研究中的应用综述[J].水利学报,2017,48(4):379-389.
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[3]谢平,陈广才,雷红富,等.论变化环境下的地表水资源评价方法[J].水资源研究,2007,28(3):1-3.
[4]王国庆,张建云,刘九夫,等.气候变化和人类活动对河川径流影响的定量分析[J].中国水利,2008(2):55-58.
[5]谢平,许斌,树安章,等.变化环境下区域水资源变异问题研究[M].北京:科学出版社,2012.
[6]李彬彬,谢平,李析男,等.基于Hurst系数与Bartels检验的水文变异联合分析方法[J].应用基础与工程科学学报,2014,22(3):481-491.
[7] MATALAS N C. Time series analysis[J]. Water Resources Research,1967,3(3):817-829.
[8]邓育仁,丁晶.长江上游河流年径流序列相依性的研究[J].地理科学,1989(3):204-212.
[9]王晓利,姜德娟,马大喜.基于MODIS NDVI时间序列的植被覆盖空间自相关分析——以山东半岛与辽东半岛区域比较研究[J].干旱区资源与环境,2013,27(10):139-144.
[10]周梅,云俊枝.多年冻土区森林流域年径流序列相依性分析[J].内蒙古林学院学报,1997(3):30-33.
[11]覃爱基.我国主要河流年径流序列相关系数的初步探讨[J].水文,1984(6):1-5.
[12]严宝文,程妍.渭河干流月径流的时历相依性研究[J].人民黄河,2013,35(11):25-27.
[13]雷晓辉,王浩,廖卫红,等.变化环境下气象水文预报研究进展[J].水利学报,2018,49(1):9-18.
[14]桑燕芳,谢平,顾海挺,等.水文过程非平稳性研究若干问题探讨[J].科学通报,2017,62(4):254-261.
[15] MAASS A,HUFSCHMIDT M M,DORFMAN R,et al. Design of water resource system[J]. Soil Science,1962,94(2):135.
[16] YEVJEVICH V M. Stochastic models in hydrology[J]. Stochastic Hydrology and Hydraulics,1987,1(1):17-36.
[17]衡思坤,郭昊坤,吴军基,等.离散序列AR模型定阶方法研究[J].微计算机信息,2012,28(9):478-479.
[18]呂锐.时间序列分析中的模型定阶策略[J].国防科技大学学报,1988(4):97-106.
[19]顾学迈,吴丹.一种基于联合信息标准的盲信噪比估计算法[J].南京航空航天大学学报,2007,39(3):363-367.
[20] PETERBICKEL,PINGZHANG,PINGZHANG. Variable selection in nonparametric regression with categorical covariates[J]. Publications of the American Statistical Association,1992,87(417):90-97.
[21]赵羽西,谢平,桑燕芳,等.基于相关系数的水文相依性变异分级方法——以自回归模型为例[J].应用生态学报,2018,29(4):1089-1097.
[22]崔振才.工程水文及水资源[M].北京:中国水利水电出版社,2008.
[23] SONUGA J O. Principle of maximum entropy in hydrologic frequency analysis[J]. Journal of Hydrology,1972,17(3):177-191.
[24]张继国,刘新仁.降水时空分布不均匀性的信息熵分析——(Ⅱ)模型评价与应用[J].水科学进展,2000,11(2):138-143.
[25] SINGH V P,RAJAGOPAL A K. A new method of parameter estimation for hydrologic frequency analysis[J]. Hydrological Science and Technology,1986,2(3):33-40.
[26]徐南荣,焦小澄.平稳时间序列模型的结构判定[J].南京工学院学报,1984(1):1-13.
[27]曾金芳,滕召胜.信息熵在曲线拟合辨识中的应用[J].电子测量与仪器学报,2012,26(2):171-176.
[28] AKAIKEI H. Information theory and an extension of maximum likelihood principle[C]//Proc. 2nd Int. Symp. on Information Theory. 1973.
[29]郑家享.统计大辞典[M].北京:中国统计出版社,1995.
[30] FISHLER E,GROSMANN M,MESSER H. Detection of signals by information theoretic criteria:general asymptotic performance analysis[J]. IEEE Transactions on Signal Processing,2002,50(5):1027-1036.
[31]陈兴钩.统计模型用AIC准则定阶的相容性问题[J].华侨大学学报(自然科学版),1989(1):6-10.
[32] AKAIKE H. Canonical correlation analysis of time series and the use of an information criterion[J]. Mathematics in Science and Engineering,1976,126:27-96.
[33] SCHWARZ G. Estimating the dimension of a model[J]. Annals of Statistics,1978,6(2):15-18.
[34]项静恬.动态和静态数据处理:时间序列和数理统计分析[M].北京:气象出版社,1991.
[35]金光炎.水文统计原理与方法[M].邯郸:中国工业出版社,1964.
[36]刘浩广,蔡绍洪.信息熵及其随机性[J].贵州大学学报(自然科学版),2007(4):350-351.
[37]谢平,唐亚松,李彬彬,等.基于相关系数的水文趋势变异分级方法[J].应用基础与工程科学学报,2014,22(6):1089-1097.
[38]沈凤麟,叶中付,钱玉美.信号统计分析与处理[M].合肥:中国科学技术大学出版社,2001.
[39]黄红梅.应用时间序列分析[M].北京:清华大学出版社,2016.
[40] LI J,TAN S,WEI Z,et al. A new method of change point detection using variable fuzzy sets under environmental change[J]. Water Resources Management,2014,28(14):5125-5138.
[41] YUE S,PILON P,CAVADIAS G. Power of the Mann-Kendall and Spearman′s rho tests for detecting monotonic trends in hydrological series[J]. Journal of Hydrology,2002,259(1):254-271.
[42] KISI O,AY M. Comparison of Mann-Kendall and innovative trend method for water quality parameters of the Kizilirmak River,Turkey[J]. Journal of Hydrology,2014,513(5):362-375.
[43]赵利红.水文时间序列周期分析方法的研究[D].南京:河海大学,2007.
[2] CHENG L,AGHAKOUCHAK A,GILLELAND E,et al. Non-stationary extreme value analysis in a changing climate[J]. Climatic Change,2014,127(2):353-369.
[3]谢平,陈广才,雷红富,等.论变化环境下的地表水资源评价方法[J].水资源研究,2007,28(3):1-3.
[4]王国庆,张建云,刘九夫,等.气候变化和人类活动对河川径流影响的定量分析[J].中国水利,2008(2):55-58.
[5]谢平,许斌,树安章,等.变化环境下区域水资源变异问题研究[M].北京:科学出版社,2012.
[6]李彬彬,谢平,李析男,等.基于Hurst系数与Bartels检验的水文变异联合分析方法[J].应用基础与工程科学学报,2014,22(3):481-491.
[7] MATALAS N C. Time series analysis[J]. Water Resources Research,1967,3(3):817-829.
[8]邓育仁,丁晶.长江上游河流年径流序列相依性的研究[J].地理科学,1989(3):204-212.
[9]王晓利,姜德娟,马大喜.基于MODIS NDVI时间序列的植被覆盖空间自相关分析——以山东半岛与辽东半岛区域比较研究[J].干旱区资源与环境,2013,27(10):139-144.
[10]周梅,云俊枝.多年冻土区森林流域年径流序列相依性分析[J].内蒙古林学院学报,1997(3):30-33.
[11]覃爱基.我国主要河流年径流序列相关系数的初步探讨[J].水文,1984(6):1-5.
[12]严宝文,程妍.渭河干流月径流的时历相依性研究[J].人民黄河,2013,35(11):25-27.
[13]雷晓辉,王浩,廖卫红,等.变化环境下气象水文预报研究进展[J].水利学报,2018,49(1):9-18.
[14]桑燕芳,谢平,顾海挺,等.水文过程非平稳性研究若干问题探讨[J].科学通报,2017,62(4):254-261.
[15] MAASS A,HUFSCHMIDT M M,DORFMAN R,et al. Design of water resource system[J]. Soil Science,1962,94(2):135.
[16] YEVJEVICH V M. Stochastic models in hydrology[J]. Stochastic Hydrology and Hydraulics,1987,1(1):17-36.
[17]衡思坤,郭昊坤,吴军基,等.离散序列AR模型定阶方法研究[J].微计算机信息,2012,28(9):478-479.
[18]呂锐.时间序列分析中的模型定阶策略[J].国防科技大学学报,1988(4):97-106.
[19]顾学迈,吴丹.一种基于联合信息标准的盲信噪比估计算法[J].南京航空航天大学学报,2007,39(3):363-367.
[20] PETERBICKEL,PINGZHANG,PINGZHANG. Variable selection in nonparametric regression with categorical covariates[J]. Publications of the American Statistical Association,1992,87(417):90-97.
[21]赵羽西,谢平,桑燕芳,等.基于相关系数的水文相依性变异分级方法——以自回归模型为例[J].应用生态学报,2018,29(4):1089-1097.
[22]崔振才.工程水文及水资源[M].北京:中国水利水电出版社,2008.
[23] SONUGA J O. Principle of maximum entropy in hydrologic frequency analysis[J]. Journal of Hydrology,1972,17(3):177-191.
[24]张继国,刘新仁.降水时空分布不均匀性的信息熵分析——(Ⅱ)模型评价与应用[J].水科学进展,2000,11(2):138-143.
[25] SINGH V P,RAJAGOPAL A K. A new method of parameter estimation for hydrologic frequency analysis[J]. Hydrological Science and Technology,1986,2(3):33-40.
[26]徐南荣,焦小澄.平稳时间序列模型的结构判定[J].南京工学院学报,1984(1):1-13.
[27]曾金芳,滕召胜.信息熵在曲线拟合辨识中的应用[J].电子测量与仪器学报,2012,26(2):171-176.
[28] AKAIKEI H. Information theory and an extension of maximum likelihood principle[C]//Proc. 2nd Int. Symp. on Information Theory. 1973.
[29]郑家享.统计大辞典[M].北京:中国统计出版社,1995.
[30] FISHLER E,GROSMANN M,MESSER H. Detection of signals by information theoretic criteria:general asymptotic performance analysis[J]. IEEE Transactions on Signal Processing,2002,50(5):1027-1036.
[31]陈兴钩.统计模型用AIC准则定阶的相容性问题[J].华侨大学学报(自然科学版),1989(1):6-10.
[32] AKAIKE H. Canonical correlation analysis of time series and the use of an information criterion[J]. Mathematics in Science and Engineering,1976,126:27-96.
[33] SCHWARZ G. Estimating the dimension of a model[J]. Annals of Statistics,1978,6(2):15-18.
[34]项静恬.动态和静态数据处理:时间序列和数理统计分析[M].北京:气象出版社,1991.
[35]金光炎.水文统计原理与方法[M].邯郸:中国工业出版社,1964.
[36]刘浩广,蔡绍洪.信息熵及其随机性[J].贵州大学学报(自然科学版),2007(4):350-351.
[37]谢平,唐亚松,李彬彬,等.基于相关系数的水文趋势变异分级方法[J].应用基础与工程科学学报,2014,22(6):1089-1097.
[38]沈凤麟,叶中付,钱玉美.信号统计分析与处理[M].合肥:中国科学技术大学出版社,2001.
[39]黄红梅.应用时间序列分析[M].北京:清华大学出版社,2016.
[40] LI J,TAN S,WEI Z,et al. A new method of change point detection using variable fuzzy sets under environmental change[J]. Water Resources Management,2014,28(14):5125-5138.
[41] YUE S,PILON P,CAVADIAS G. Power of the Mann-Kendall and Spearman′s rho tests for detecting monotonic trends in hydrological series[J]. Journal of Hydrology,2002,259(1):254-271.
[42] KISI O,AY M. Comparison of Mann-Kendall and innovative trend method for water quality parameters of the Kizilirmak River,Turkey[J]. Journal of Hydrology,2014,513(5):362-375.
[43]赵利红.水文时间序列周期分析方法的研究[D].南京:河海大学,2007.