基于粗糙集理论的企业财务危机预测模型及实证研究
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摘要
国内外许多研究得出的结论已经表明，财务数据和财务指标可用于预测企业的财务危机或破产风险。在财务危机预测领域，就研究方法而言，已经趋于稳定，近几年来始终没有重大的突破，相关的研究只是从技术细节上不断的完备，目前仍然存在着一些问题，如：预测变量的选择、多重共线性等问题，始终没有得到有效的解决。要有效的解决现存问题需要在预测方法上有比较大的突破。
国内的相关研究方法基本与国外接轨，创新之处非常有限。
本文将粗糙集理论和信息熵概念引入财务危机预测领域，建立一种基于粗糙集理论的企业财务危机预测模型，试图一定程度避免相关问题的产生。在预测变量的选择上，首先采用统计方法进行财务指标的初步筛选，然后设计出一个基于信息熵的属性约简算法对财务指标进行进一步筛选，以确定进入模型的变量。通过计算条件属性和决策属性的依赖度来确定条件属性的重要程度，对其进行归一化处理后即得到预测变量的权系数，进而确定综合预测模型。
本文的检验方法与以往的研究不同，采用两步检验的方式说明模型的预测效果。首先采用小样本进行检验，然后采集尽可能多的样本再次对模型进行检验，以说明预测模型的稳定性。在每一步检验的同时，又选取常用的Fisher判别方法与本模型进行了预测效果的对比分析。
实证结果表明，本文建立的模型效果很好，采用相同的财务信息，其预测效果优于Fisher模型。在发生财务危机（ST）前一年，采用小样本检验,其正确判别率达到了100％；采用大样本检验，选取了878家上市公司数据，误判数只有9个。即使是发生ST的前四年，采用小样本检验，其误判率只有21％；随机选取273家公司进行大样本检验，其误判数也只有22个。
论文主要包括五个部分：第一部分主要介绍了论文的研究背景和国内外研究现状；第二部分介绍了传统财务危机预测模型并对其进行了评析；第三部分介绍了粗糙集理论和信息熵的相关概念；第四部分建立了基于粗糙集的预测模型，重点介绍了基于信息熵的预测变量筛选算法。第五部分对模型进行了实证分析。
The conclusions elicited by so many studies at home and abroad indicated that the financial data and financial index can be used to predict the financial crisis or bankruptcy risk of an enterprise, and in case of the methods in the field of financial risk prediction has inclined to be stability, and no important breakthrough in recent years. Correlated studies are only inconstant to mature in technical details, and some existing problems, for instance the selection of prediction variables, multicollinearlity etc, still remain unsolved effectively up to today. To settle the involved problems virtually, the decisive breakthrough in the study methods is needed!
The correlated study methods of our home country are primarily following the abroad, and the innovations are limited!
This paper introduces the idea of rough sets theory and information entropy to build up a model, which can be used to predict the financial risk of an enterprise, in case some correlated affairs occur in some degree. Concerning the chosen of the prediction variable, firstly, this paper employs statistical technic to elementarily filter the financial indexes, then plan an attribute reduction arithmetic based on the property of information entropy to simplify it, so as to elicit the variables involved in the model. The technic which I use to elicit the coefficient of the prediction variable is that I firstly compute the dependance of condition attribute and decision attribute, then work out the importance of condition property(financial index), finally unify this importance and get the coefficient of prediction variable.
Different from the former' verifying method of the model, this paper employ a two-step checkup mode to show the prediction effect of this model. In the first step, I check it with the small sample set, then collect samples as many as possible to check it again to testify the stability. Accompanied by each step, Fisher discriminant analysis is employed to make contrast analysis to the prediction result.
Study result has indicated that, the result of this model is well enough. With the same financial information, it does better than Fisher discriminant
analysis. By the small sample checked, this model reach a correct differentiation ratio of 100％ before one year of the financial risk(ST) happens; and by the large sample checked, I choose the data come from 878 stock market corporations, and the number of miscarriage of justice is only 9. Even before 4 years of ST, with small sample checking, the miscarriage of justice ratio is only 21％. Selecting 273 enterprises randomly to proceed large sample check, the number of miscarriage of justice is 22.
The paper consists of five part: the first part mainly introduces the background and research situation in the home and abroad; and the second part reviews and analyses traditional models on financial crisis prediction; then inducts two correlated concept, named rough sets theory and information entropy; and in the first part the paper builds up the prediction model based on rough sets theory, and especially describe the filtering technic based on the information entropy; finally the fifth part analyses the model with the study.
国内的相关研究方法基本与国外接轨，创新之处非常有限。
本文将粗糙集理论和信息熵概念引入财务危机预测领域，建立一种基于粗糙集理论的企业财务危机预测模型，试图一定程度避免相关问题的产生。在预测变量的选择上，首先采用统计方法进行财务指标的初步筛选，然后设计出一个基于信息熵的属性约简算法对财务指标进行进一步筛选，以确定进入模型的变量。通过计算条件属性和决策属性的依赖度来确定条件属性的重要程度，对其进行归一化处理后即得到预测变量的权系数，进而确定综合预测模型。
本文的检验方法与以往的研究不同，采用两步检验的方式说明模型的预测效果。首先采用小样本进行检验，然后采集尽可能多的样本再次对模型进行检验，以说明预测模型的稳定性。在每一步检验的同时，又选取常用的Fisher判别方法与本模型进行了预测效果的对比分析。
实证结果表明，本文建立的模型效果很好，采用相同的财务信息，其预测效果优于Fisher模型。在发生财务危机（ST）前一年，采用小样本检验,其正确判别率达到了100％；采用大样本检验，选取了878家上市公司数据，误判数只有9个。即使是发生ST的前四年，采用小样本检验，其误判率只有21％；随机选取273家公司进行大样本检验，其误判数也只有22个。
论文主要包括五个部分：第一部分主要介绍了论文的研究背景和国内外研究现状；第二部分介绍了传统财务危机预测模型并对其进行了评析；第三部分介绍了粗糙集理论和信息熵的相关概念；第四部分建立了基于粗糙集的预测模型，重点介绍了基于信息熵的预测变量筛选算法。第五部分对模型进行了实证分析。
The conclusions elicited by so many studies at home and abroad indicated that the financial data and financial index can be used to predict the financial crisis or bankruptcy risk of an enterprise, and in case of the methods in the field of financial risk prediction has inclined to be stability, and no important breakthrough in recent years. Correlated studies are only inconstant to mature in technical details, and some existing problems, for instance the selection of prediction variables, multicollinearlity etc, still remain unsolved effectively up to today. To settle the involved problems virtually, the decisive breakthrough in the study methods is needed!
The correlated study methods of our home country are primarily following the abroad, and the innovations are limited!
This paper introduces the idea of rough sets theory and information entropy to build up a model, which can be used to predict the financial risk of an enterprise, in case some correlated affairs occur in some degree. Concerning the chosen of the prediction variable, firstly, this paper employs statistical technic to elementarily filter the financial indexes, then plan an attribute reduction arithmetic based on the property of information entropy to simplify it, so as to elicit the variables involved in the model. The technic which I use to elicit the coefficient of the prediction variable is that I firstly compute the dependance of condition attribute and decision attribute, then work out the importance of condition property(financial index), finally unify this importance and get the coefficient of prediction variable.
Different from the former' verifying method of the model, this paper employ a two-step checkup mode to show the prediction effect of this model. In the first step, I check it with the small sample set, then collect samples as many as possible to check it again to testify the stability. Accompanied by each step, Fisher discriminant analysis is employed to make contrast analysis to the prediction result.
Study result has indicated that, the result of this model is well enough. With the same financial information, it does better than Fisher discriminant
analysis. By the small sample checked, this model reach a correct differentiation ratio of 100％ before one year of the financial risk(ST) happens; and by the large sample checked, I choose the data come from 878 stock market corporations, and the number of miscarriage of justice is only 9. Even before 4 years of ST, with small sample checking, the miscarriage of justice ratio is only 21％. Selecting 273 enterprises randomly to proceed large sample check, the number of miscarriage of justice is 22.
The paper consists of five part: the first part mainly introduces the background and research situation in the home and abroad; and the second part reviews and analyses traditional models on financial crisis prediction; then inducts two correlated concept, named rough sets theory and information entropy; and in the first part the paper builds up the prediction model based on rough sets theory, and especially describe the filtering technic based on the information entropy; finally the fifth part analyses the model with the study.
引文
[1] 詹姆斯.德阿克，企业德泛风险管理--动态的处理风险与机遇的系统化策略[M]，长春：吉林人民出版社，2001:3-5
[2] 黄岩，李元旭.上市公司财务失败预测实证研究,系统工程理论方法应用，2001.1：45-51
[3] 财政部注册会计师考试委员会办公室编，财务成本管理，北京：经济科学出版社，2002.3
[4] Beaver，W. H.，Financial Ratios as Predictors of Failure，Supplement to Journal of Accounting Research 1966.4:71-111
[5] Altman，E. I.，Financial Ratios，Discriminant Analysis，and the Prediction of Corporate Bankruptcy，Journal of Finance 1968.9:589-609.
[6] Altman，E. I.，R.Haldeman.and P.Narayanan，ZETA Analysis: A New Model to Identify Bankruptcy Risk of Corporations，Journal of Banking and Finance 1977.1:29-54
[7] Edmister，R. O，. An Empirical Test of Financial Ratio Analysis for Small Business Failure Prediction，Journal of Financial and Quantitative Analysis,1972.3:204-227
[8] James O. Horrigan，An Evaluation of the Usage of Ratios in External Financial Statement Analysis，The University of Chicago，1963.1
[9] Beaver W. Market prices, financial ratios, and the prediction of failure . Journal of Accounting Research, 1968.1: 179-192.
[10] Aharony, J., C.P.Jones, and I.Swary,An Analysis of Risk and Return Characteristics of Corporate Bankruptcy Using Capital Marker Data,Journal of Finance 1980.9: 1001-1016.
[11] Warner,J.B.,Bankruptcy,Absolute Priority,and the Pricing of Risky Debt Claims, Journal of Financial Economics 1977.5:239-276.
[12] Fraydman H , Altman E. , Kao D. introducing recursive partitioning for financial classfication: the case of financial distress. Journal of Banking & Finance, 1985,11:269-291.
[13] Ohlson，J. A.，Financial Ratios and the Probabilistic Prediction of Bankruptcy，Journal of Accounting Research 1980.3:109-131.
[14] 何沛利、章早立等， 立体空间下的全新财务危机远期预警模型，广发证券股份有限公司，深圳证券交易所第五届会员单位、基金管理公司研究成果获一等奖论文，2003
[15] Barbro Back， Choosing Bankruptcy Predictors:Using Discriminant Analysis, Logit Analysis, and Genetic Algorithms, Turku Centre for Computer Science Technical Report No.40, 1996.9.
[16] Yaon Y,Swles C T, A comparison of discriminant analysis versus artificial neural networks. Journal of Peratia Research Society, 1993,44:51-60.
[17] Benzing, Cythia. Using Discriminant Analysis to Predict Financial Distress . International Advances in Economic Research, 2000,6: 591～593.
[18] Andreas Charitou, Lenos Trigeorgis.Option-Based Bankruptcy Prediction, University of Cyprus Working Paper, Social Science Research Network Electronic Paper Collection. 2000
[19] 陈静，上市公司财务恶化预测的实证分析.会计研究，1999.4：31-38.
[20] 吴世农，卢贤义. 我国上市公司财务困境的预测模型研究，经济研究， 2001.6：46-55.
[21] 高培业，张道奎，企业失败判别模型实证研究.统计研究，2000.10：46-51.
[22] 张爱民，祝春山，许丹键.上市公司财务失败的主成分预测模型及其实证研究.金融研究，2001.3：10-25
[23] 张玲. 财务危机预警分析判别模型， 数量经济技术经济研究，2000.3：49-51
[24] 尹侠，肖序，胡永康.上市公司财务预警的实证分析，财经理论与实践, 2001.11：83-87，
[25] 陈瑜. 对我国证券市场ST公司预测的实证研究，经济科学, 2000.6 ：57-67
[26] 张鸣，张艳. 财务困境预测的实证研究与评述，财经研究，2001.12：29-34
[27] 卢宇林等.上市公司财务失败预警系统实证分析，兴业证券股份有限公司，深圳证券交易所第四届会员单位、基金管理公司研究成果评奖论文,2002.
[28] 蔡红艳，韩立岩.上市公司财务状况判定模型研究，审计研究，2003.1：62-64
[29] 肖华，李建华.关于建立国有企业财务预警系统的探讨，厦门大学学报（社科版），1999.4，74-80
[30] 何清波.企业财务失败的原因、预警与补救，中央财务金融学院，1996.12，42-46
[31] Dimitras A. , Slowinski R. , Susmaga R. .Zopounidis C. Business failure prediction using rough sets. European Journal of Operational Research 1999.(114): 263～280
[32] 柳炳祥、盛昭翰.基于粗神经网络的企业财务危机预警方法，中国工程科学，2002.8：58-62
[33] 韩祯祥、张琦,文福栓，粗糙集理论及其应用综述，控制理论与应用，1999，2,153-157
[34] 肖健华，吴今培，杨叔子.基于启发式知识的属性约简方法及其在评价体系中的应用，系统工程，2002，1，92-96
[35] 石骁，赵庆飞，基于粗糙集理论的模糊综合评判权值确定，西南石油学院学报，2001.6，16-18
[36] 张文彤 主编.SPSS11统计分析教程（高级篇），北京：希望电子出版社，2002.6： 177-180
[37] 王济川、郭志刚，Logistic 回归模型-方法与应用，北京：高等教育出版社2001版，28-33。
[38] Pawlak Z, Rough sets. International Journal of Inform ation and Computer Science, （11）1982：341-356
[39] 张琦,韩祯祥,文福拴.一种基于粗糙集方法的电力系统故障诊断/警报处理的新方法.中国电力,1998,31(4):32-38
王珏,苗夺谦,周育键.关于Rough set理论与应用的综述.模式识别与人工智
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[51] 胡永宏，贺思辉，综合评价方法。 北京：科学出版社，2000，28-30
[2] 黄岩，李元旭.上市公司财务失败预测实证研究,系统工程理论方法应用，2001.1：45-51
[3] 财政部注册会计师考试委员会办公室编，财务成本管理，北京：经济科学出版社，2002.3
[4] Beaver，W. H.，Financial Ratios as Predictors of Failure，Supplement to Journal of Accounting Research 1966.4:71-111
[5] Altman，E. I.，Financial Ratios，Discriminant Analysis，and the Prediction of Corporate Bankruptcy，Journal of Finance 1968.9:589-609.
[6] Altman，E. I.，R.Haldeman.and P.Narayanan，ZETA Analysis: A New Model to Identify Bankruptcy Risk of Corporations，Journal of Banking and Finance 1977.1:29-54
[7] Edmister，R. O，. An Empirical Test of Financial Ratio Analysis for Small Business Failure Prediction，Journal of Financial and Quantitative Analysis,1972.3:204-227
[8] James O. Horrigan，An Evaluation of the Usage of Ratios in External Financial Statement Analysis，The University of Chicago，1963.1
[9] Beaver W. Market prices, financial ratios, and the prediction of failure . Journal of Accounting Research, 1968.1: 179-192.
[10] Aharony, J., C.P.Jones, and I.Swary,An Analysis of Risk and Return Characteristics of Corporate Bankruptcy Using Capital Marker Data,Journal of Finance 1980.9: 1001-1016.
[11] Warner,J.B.,Bankruptcy,Absolute Priority,and the Pricing of Risky Debt Claims, Journal of Financial Economics 1977.5:239-276.
[12] Fraydman H , Altman E. , Kao D. introducing recursive partitioning for financial classfication: the case of financial distress. Journal of Banking & Finance, 1985,11:269-291.
[13] Ohlson，J. A.，Financial Ratios and the Probabilistic Prediction of Bankruptcy，Journal of Accounting Research 1980.3:109-131.
[14] 何沛利、章早立等， 立体空间下的全新财务危机远期预警模型，广发证券股份有限公司，深圳证券交易所第五届会员单位、基金管理公司研究成果获一等奖论文，2003
[15] Barbro Back， Choosing Bankruptcy Predictors:Using Discriminant Analysis, Logit Analysis, and Genetic Algorithms, Turku Centre for Computer Science Technical Report No.40, 1996.9.
[16] Yaon Y,Swles C T, A comparison of discriminant analysis versus artificial neural networks. Journal of Peratia Research Society, 1993,44:51-60.
[17] Benzing, Cythia. Using Discriminant Analysis to Predict Financial Distress . International Advances in Economic Research, 2000,6: 591～593.
[18] Andreas Charitou, Lenos Trigeorgis.Option-Based Bankruptcy Prediction, University of Cyprus Working Paper, Social Science Research Network Electronic Paper Collection. 2000
[19] 陈静，上市公司财务恶化预测的实证分析.会计研究，1999.4：31-38.
[20] 吴世农，卢贤义. 我国上市公司财务困境的预测模型研究，经济研究， 2001.6：46-55.
[21] 高培业，张道奎，企业失败判别模型实证研究.统计研究，2000.10：46-51.
[22] 张爱民，祝春山，许丹键.上市公司财务失败的主成分预测模型及其实证研究.金融研究，2001.3：10-25
[23] 张玲. 财务危机预警分析判别模型， 数量经济技术经济研究，2000.3：49-51
[24] 尹侠，肖序，胡永康.上市公司财务预警的实证分析，财经理论与实践, 2001.11：83-87，
[25] 陈瑜. 对我国证券市场ST公司预测的实证研究，经济科学, 2000.6 ：57-67
[26] 张鸣，张艳. 财务困境预测的实证研究与评述，财经研究，2001.12：29-34
[27] 卢宇林等.上市公司财务失败预警系统实证分析，兴业证券股份有限公司，深圳证券交易所第四届会员单位、基金管理公司研究成果评奖论文,2002.
[28] 蔡红艳，韩立岩.上市公司财务状况判定模型研究，审计研究，2003.1：62-64
[29] 肖华，李建华.关于建立国有企业财务预警系统的探讨，厦门大学学报（社科版），1999.4，74-80
[30] 何清波.企业财务失败的原因、预警与补救，中央财务金融学院，1996.12，42-46
[31] Dimitras A. , Slowinski R. , Susmaga R. .Zopounidis C. Business failure prediction using rough sets. European Journal of Operational Research 1999.(114): 263～280
[32] 柳炳祥、盛昭翰.基于粗神经网络的企业财务危机预警方法，中国工程科学，2002.8：58-62
[33] 韩祯祥、张琦,文福栓，粗糙集理论及其应用综述，控制理论与应用，1999，2,153-157
[34] 肖健华，吴今培，杨叔子.基于启发式知识的属性约简方法及其在评价体系中的应用，系统工程，2002，1，92-96
[35] 石骁，赵庆飞，基于粗糙集理论的模糊综合评判权值确定，西南石油学院学报，2001.6，16-18
[36] 张文彤 主编.SPSS11统计分析教程（高级篇），北京：希望电子出版社，2002.6： 177-180
[37] 王济川、郭志刚，Logistic 回归模型-方法与应用，北京：高等教育出版社2001版，28-33。
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[39] 张琦,韩祯祥,文福拴.一种基于粗糙集方法的电力系统故障诊断/警报处理的新方法.中国电力,1998,31(4):32-38
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