Business Bankruptcy Prediction Based on Survival Analysis Approach

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1 Busess Bakruptcy Predcto Based o Survval Aalyss Approach ABSTRACT Mg-Chag Lee Natoal Kaohsug Uversty of Appled Scece, Tawa Ths study sampled compaes lsted o Tawa Stock Exchage that examed facal dstress betwee 2003 ad It uses the survval aalyss to fd the ma dcators whch ca expla the busess bakruptcy Tawa. Ths paper uses the Cox Proportoal Hazard Model to assess the usefuless of tradtoal facal ratos ad market varables as predctors of the probablty of busess falure to a gve tme. Ths paper presets emprcal results of a study regardg 12 facal ratos as predctors of busess falure Tawa. It showed that t does ot eed may ratos to be able to atcpate potetal busess bakruptcy. The facal dstress probablty model s costructed usg Proftablty, Leverage, Effcecy ad Valuato rato varables. I the proposed steps of busess falure predcto model, t used detal SAS procedure. The study proves that the accuraces of classfcato of the mode overall accuracy of classfcato are 87.93%. KEYWORDS Busess Falure predcto; Survval Aalyss; Cox Proportoal Hazard model; Logstc model 1. INTRODUCTION Busess Falure Predcto (BFP) models are estmato of the bakruptcy probablty of a frm usg a set of covarates, such as facal ratos, Captal turover, Captal turover, etc [77]. I past decades, BFP has bee a topc research for busess ad corporate orgazatos. Ivestors or credtors, borrowg orgazatos ad govermets are creasg terest to predct of corporate bakruptcy [26]. BFP help to avod ledg to (or vestg ) busess lkely to fal, early detfcato of falg busess by regulatory bodes, ad more accurate scorg models for ratg ageces. Bakruptcy predcto models use statstcal aalyss ad data mg techque to ehace the decso support tool ad mprove decso makg [68]. Statstcal busess falure predcto models attempt to predct the busess falure or success. The Multple dscrmat aalyss (MDA) has bee the most popular approaches, but there eed a large umber of alteratve techques avalable ([18], [37], [42]). Such as the data mg techques clude decso tree, eural etworks (NNs), support vector mache (SVM), fuzzy system, rough set theory, geetc algorthm (GA) [68]. Varous researches have demostrated the artfcal tellgece (AI) techques such as artfcal eural etworks (ANNs) ca serve as a useful tool bakruptcy predcto [61]. Back propagato eural etwork (BPNN) was used bakruptcy predcto. Before that BPNN some of the techques followed such as k-earest eghbor ad the tree DOI: /jcst

2 algorthm (ID3) but offered better predctve compare tha compared models. Multvarate cumulatve sum (CUSUM) s a sequetal procedure to predct a busess tedecy towards falure. A survval aalyss (SA) techque s the term appled to a dyamc statstcal tool used to aalyss the tme tll a certa evet [18]. SA uses the Cox proportoal hazard model to aalyss survval probablty ad falure tmes; t s oe dyamc model approach [53]. SA techques have used to exame the drvers behd the survval of Iteret busess ([29], [30]). Dscrmat aalyss (DA) ad Logt aalyss (LA) were foud to be slghtly superor predctors to the Cox proportoal hazard model [27]. Nevertheless, Late ad Luoma [33] argued that the SA approach was more atural, flexble, ad approprate ad used more formato Busess Falure predcto. Keasey et al. [31] also recommeded that SA techques be used BFP. Yap et al. [69] use facal rato ad logstc regresso for evaluatg compay falure Malaysa. The models of eterprse credt rsk modes clude statstcal model, eural etwork, learg vector, soft-computg, ad hybrd models. Table 1 deoted as eterprse credt rsk model. Eterprse credt rsk evaluato models ths study are Neural etworks, Bayesa classfer, Dscrmat aalyss, Logstc regresso, K-earest eghbor, Decso tree, Case base reasog, Support vector mache, Software computg, Fuzzy rule-based system, Geerc algorthms, Grey relato, ad Hybrd models. Table 1: Eterprse credt rsk evaluato models Category Area Some Approach Statstcal model Neural Networks Learg vector Softcomputg Parametrc Statstcal Method No-Parametrc Statstcal Method Mache learg Mache learg Reducto attrbutes 1. Dscrmat aalyss 2. Lear mult dscrmat aalyss 3. Logstc regresso 4. Bayesa rsk Dscrmat aalyss 1. K- earest eghbor 2. Cluster aalyss 1. Multlayer percepto 2. Back propagato 3. Radal fucto eural etwork 3. Probablstc eural etwork 4. Self-orgazed competto Support Vector Mache 1. Rough sets of reducto kowledge 2. Grey relatoal of reducto kowledge Altma [3]; Ohlso [47]; Yap et al. [69]; Stefaescu et al. [56]; Tabachck ad Fdell [59]; Lag ad X [36] Ice, ad Akta [24]; Islam et al. [25]; Lau [34]; Su ad LI [58] Islam et al. [25; Che [13]; Lopez [39]; Mues et al. [44]; Sarkar ad Srram [50]; Stefaescu et al. [56]; Tam ad Kag [60] ; Che [12]; Odom ad Sharda [46] Zhou et al. [72]; Che et al. [11] ; Km ad Soh [32]; Sh et al. [52] Dmtras et al. [17]; Cheg et al. [14]; Ba ad Mazlack [6]; Hu [23]; Lu et al.[38] ; Tug et al. [62]; 104

3 Survval aalyss (SA) Hybrd models Tme to evet data aalyss Combato of two or more methods 3. Geetc algorthm of reducto kowledge 4. Fuzzy-Rough Sets Approach 1. Credt rsk modelg based o SA 2. Corporate credt rsk ad the macro ecoomy 1. Rough - K Nearest Neghbor 2. Rough Sets Neural Network 3. Fuzzy-Rough Sets - Nearest Neghbor 4. Fuzzy- Nearest Neghbor 5. Support Vector Mache wth Nearest Neghbor 6. GA-based eural etwork approach 7. At Coloy Algorthm based o quck-reduct algorthm We et al. [64]; Wog et al. [65]; Zhao [72]; Xhu ad Zhog [67] Stepaova, ad Thomas [57]; Atoaks ad Sfakaaks [4]; Cao et al. [8]; Soh et al. [55] Tug et al. [62]; Wag et al. [63]; We ad Zhag[64]; Wog et al. [65]; Xao et al. [66]; Chaduhur ad De [10]; Tam ad Kag [60]; Yu et al. [70]; Zhag et al. [71]; Zhou ad Ba [73]; Zhou et al. [75] The most useful beefts to SA are: (1) I the modelg process, SA s able to take tme-varyg varables to accout [22]. Ths s doe through proportoal hazard models [5]. (2) SA s ot restrcted by the assumpto that the dstrbutos of the varables the data eed to be ormal [54]. (3) SA oly produces postve predctos of tme [21]. The tme-varyg has the potetal to ot follow a ormal dstrbuto. It eeds to be postve predctos ad s flueced by tme-varyg varables. The major cotrbuto of SA methods s estmato procedures that cosder chages the value of covarates over tme [35]. Thus, SA approaches to BFP dfferet from the other approaches metoed above [18]. 3. MERHODOLOGY 3.1 Logt model I settg up the logstc regresso model, frst establsh the fudametal model for ay multple regresso aalyss. The outcome varable s assumed as a lear combato of a set of predctors. If outcome varable s Y, ad a set of predctor varables are X 1, X 2,..., X, the Logt model s: [1] Y 0 1X1 2 X 2... X 0 j X j (1) j1 105

4 Where 0 s the expected value of Y whe X s set 0. j s the regresso coeffcet for each correspodg predctor varable X j. s the error of the predcto. Defes (x) as the probablty that Y = 1. Smlarly, 1- (x) s the probablty that Y = 0. These probabltes are wrtte the followg form: ( x ) P ( Y 1 X, X 2,..., X ) ( x) P( Y 0 X, X,..., X ) (2) Ths model for the atural logarthm of the ( x) 1 ( x) s: P( Y 1 X 1, X 2,..., X ) ( x) l l 0 j X 1 P( Y 1 X, X,..., X ) 1 ( x) 1 2 j1 j (3) Usg the verse of the Logt trasformato of (3), t obtas at the followg: P( Y 1 X, X 1 2,..., X ) e 1 e 0 j X j j1 0 j X j j1 1 e 1 ( 0 j X j ) j1 (4) Thus, (4) s a logstc regresso model, the codtoal mea s betwee 0 ad 1. Now, t wll ft the logstc regresso model to the data. Frstly, t must establsh a techque for estmatg the parameters. The maxmum lkelhood s the method of parameter estmato logstc regresso model. Ths method costructs the lkelhood fucto, whch expresses the probablty of the observed data as a fucto of the ukow parameters. Ths process wll have selected the estmators (4). For a set of observatos the data ( x, y ), the cotrbuto to the lkelhood fucto s ( x ), where y 1, ad 1 ( x ), where y 0. The followg equato results for the cotrbuto to the lkelhood fucto for the observato x, ) s x ) : ( y ( y ( ) ( ) 1 y x [1 ( ) x x ] (5) The observatos are assumed to be depedet of each other so t ca multply ther lkelhood cotrbutos to obta the complete lkelhood fucto l (B). The result s gve (6). l( B) ( ) (6) 1 x Where B s the collecto of parameters ( 0, 1,..., ) ad l(b) s the lkelhood fucto of B. 106

5 Maxmum lkelhood estmates (MLE s) ca be obtaed by calculatg the B whch maxmzes l (B). However, to smply the mathematcs, from the logarthm of (6) before fdg the value whch maxmzes the lkelhood fucto. As show (7). L(B) s deoted the log lkelhood expresso. L( B) l[ l( B)] ( y 1 l[ ( x )] (1 y ) l[1 ( x )]) (7) It employs the techques of calculus to determe the value of B based o maxmum of L (B). Ths s doe by dfferetatg (3) wth respect to 0, 1,..., ad settg the resultg dervatves equal to zero. These equatos are called lkelhood estmatos, ad there s +1 equato. They are of the followg form: 1 y ( ) 0, for the tercept 0, ad x,..., x 1. k 1 [ y ( x )] 0, for the predctor varables, The soluto ca be solvg by usg computer programs such as SAS or SPSS. It performs the logstc regresso aalyss of the data for ths study ad wll calculate the maxmum lkelhood estmates. 3.2 Cox s PH model [15] Accordg the assumpto about the relatoshp betwee the hazard (or survval) fucto ad the set (vector) of explaatory varables ( X ), there have varous models. Thus, the geeral T T regresso fucto ca be wrtte as h( t) g( t, X ), where X s the traspose of X. s the vector of explaatory varable coeffcets. I SA models, t s customary to estmate the hazard rate, ad the derve the survval rate are requred by usg regresso model. Two ma types of regresso models are SA model. These types are the proportoal hazards (PH) ad accelerated falure tme (AFT) models, both of whch have fully parametrc ad sem-parametrc verso. A parametrc regresso model based o the expoetal dstrbuto: logeh ( t) 1x1 2x2... x (8) Or equvaletly, h ( t) exp( 1x1 2x 2... k xk ) x e e e x e k xk (9) Where dexes subjects; x 1, x2,... xk s the values of covarates for the th subject Ths model s parametrc because, oce the regresso parameters, 1, 2,..., k are specfed, the hazard fucto h (t) s fully characterzed by the model. The costat represets a kd of basele hazard, (9), sce log e h ( t), or equvaletly, h ( t) e whe all of the x s are 0. Other parametrc hazard regresso models are based o other dstrbutos (Gompertz ad k k 107

6 Webull dstrbuto) commoly used modelg survval data. The Cox model superseded full parametrc hazard regresso models, whch leaves the basele hazard fucto uspecfed: Or equvaletly, logeh ( t) ( t) 1x1 2x2... x (10) h t) h ( t)exp( x x... x ) (11) ( k k To estmate the model parameters, the maxmum lkelhood estmates are derved by maxmzg a lkelhood fucto. Ths Cox model [17] s termed sem-parametrc because whle the basele hazard ca take by form, the covarates eter the model through the lear predctor... x (12) 1x1 2x2 I (12), there s o costat term (tercept) the lear predctor; the costat s absorbed the basele hazard. The Cox regresso model s also a proportoal hazard model. Cosder two observatos, ad ', that dffer ther x-values, wth respectve lear predctors... x ad 1x1 2x2 k k ' 1x ' 1 The hazard ratos for these two observatos are: k k k k (13) ( ) 0( ) t h t e ' e ' ( t) ' h0( t) e h h 2x '...k x 2 ' k (14) I (14), the rato s costat over tme. Therefore, the Cox model ca easly accommodate tmedepedet covarates. The Cox model accouts for survval tmes, thus, t uses more formato the the logstc model. The Cox PH model allows cesored observatos ad corporates survval tmes. A Cox PH model therefore uses more formato tha a logstc regresso model. 3.3 Goodess-of-ft test A set of covarates the Cox PH model ca be tme-depedet (or tme varyg) covarates. Used SAS (or SPSS) to perform the Cox PH model aalyss of the data for ths paper ad wll calculate the maxmum lkelhood estmates. Used lkelhood rato test to see the varables cluded the fal model are sgfcat explag some of varablty data. The Ch-Square statstc s the dfferece -2 Log Lkelhood (-2LL) betwee the fal model ad a reduced model. The ull hypothess s that all parameters ( 1, 2..., k ) of the effect are 0. Ths test s comparable to oval F test for regresso aalyss. The hypothess testg s as follows: H0 : k 0; H 1 :~ H 0 Where s the parametrc estmato of explaatory varable The statstc quatty of the aforesad hypothess testg s -2 Log Lkelhood (= -2Log (L(0)- 108

7 L( )) whch observes 2 ( k ), where L(0) s the lkelhood fucto value uder the ull hypothess, whle L( ) s the lkelhood fucto value cosderato of the whole model. R 2 s a tutve measure of how well model predcts the values of the depedet varables [69]. R 2 the Cox regresso s a pseudo measure of assocato betwee the respose varable ad covarates. I geeral, hgher R 2 value meas the model s ft for aalyss of samplg. Sce lght that maxmum of 1 caot be obtaed usg Cox & Sell R 2 for measuremet; Nagelkerke [45] proposed a modfcato of Cox & Sell R 2. Cox & Sell R 2 : 2 L(0) R 1 [ ] 2 N cs 1 exp[( L(0) L( )) * 2 / N ] (15) L( ) Nagelkerke R 2 : R 2 2 / max 2 N Rcs Rcs (16) Where L (0) = the lkelhood fucto value cotag oly tercept; L ( ) fucto value cosderato of the whole model; N= sample sze, 4. COX MODEL PREDICTIVE ABILITY = the lkelhood 2 2 max R cs 1 [ L(0)] The most mportat characterstcs of a BFP model are ts producto of accuracy. Type Ⅰ error refer to the stuato whe actual falure compay s classfed as o falures compay, ad Type Ⅱ error refer to o falure compay s classfed as o falures compay. Type error s more mportat tha Type error. The objectves of predctve of accuracy should be to reduced Type error whle keep Type error. The reaso for ths s that Type Ⅱ error oly creates a lost opportuty cost from ot dealg wth a successful busess, for example, mssed potetal vestmet gas. I cotrast, due to volvemet wth a busess that wll fal, Type error results a realzed facal loss, for example, losg all moey vested a mpedg bakrupt busess [18]. The method used for calculatg the accuracy of classfyg dstressed compaes ad odstressed compaes s llustrated Table 2, whch C deotes the umber of TypeⅠ error, that s the umber of dstressed compaes the sample based o actual observato that were msclassfed as a o-dstressed compay. B deotes the umber of Type Ⅱ error that s the umber of o-dstressed compaes the sample based o actual observato that were msclassfed as a dstressed compay. A ad D represet respectvely the umber of odstressed ad dstressed accurately classfed by the models [34]. By determg accuracy of classfcato, we ca lear about whether the costructed model s the optmal predcto model. 109

8 Table 2: Robustess of model No-dstressed No-dstressed compay Dstressed compay Observed value No-dstressed compay A B E Dstressed compay C D F G Overall accuracy of classfcato Accuracy of Classfcato Note: 1. The accuracy of classfcato of o-dstressed compay s expressed by E A /( A B) 2. The accuracy of classfcato of dstressed compay s expressed by F D /( C D) 3. The oval accuracy of classfcato s G ( A D) /( A B C D) 5. EMPIRICAL RESEARCH I ths secto, the study frst performs descrptve statstc of the samplg ad Covarates, ad follows by the costructo of busess falure predcto model based o Cox model ad aalyss of emprcal results. I order to better aalyze the effect of the Cox model predcted, we radom select the stock market lsted compay's tradtoal maufacturg Tawa. I sub-secto, goodess-of-ft test s carred out ad robustess of the model s examed usg accuracy of classfcato. The proposed steps of busess falure predcto model are: Step 1: Defto of varables Step 2: Samplg ad data Step 3: Reduced the umber of facal rato Step 4: Goodess-of-ft test Step 5: Robustess of model predcto accuracy 5.1 Selecto of Varables The ma goal of ths research s to assess the emprcal classfcato ad predcto accuracy of the COX SA model whe appled to BFP. Karels ad Prakash [28] suggested a careful selecto of ratos to be used the developmet of bakruptcy predcto model. A set of covarates used ths study cludes a combato of facal ratos ad market varables [20]. I facal reportg aalyss, [19] suggest fve factors for evaluato eterprse facal falure. Facal ratos have bee wdely used explag the possblty of busess facal dstress ([3], [7], [9], [43], [47], [48], [49], ad [76]). Table 3 s The 12 ratos selected ths study. 110

9 Table 3: The 12 ratos selected ths study Table 3 shows the detals ad defto of covarates used ths study. 12 facal ratos are used ths study. The Proftablty ratos clude EBIT marg (EBT), Retur to equty (ROE), ad Retur o assets (ROA). Curret rato (CUR) ad Quck rato (QUK) wll be used ths study order to measure the lqudty of the frms. Two types of Leverage ratos are Debt rato (DET) ad Debt to equty rato (DER), two types of Effcecy ratos are Fxed asset turover (FAT) ad Captal turover (CAT) ad three types of Valuato ratos are Prce to sales rato (PSR), prce eargs rato (PER), ad prce to book value (PBV). 5.2 Data collecto ad Sample The sample ths research s radom selecto the stock market lsted compay's tradtoal maufacturg Tawa. I order to cosder the survval problem, the choce of lsted compaes lsted o the Tawa Stock Exchage usg aual data o facal ratos for the perod I order to better aalyze the effect of the Cox model predcted, ths study estmated that from 2003 to 2009 sample was dvded to estmatg samples ad forecastg samples. Ths paper select sample lsted compaes from 2003 to 2006 for estmatg sample. There are 56 facally dstressed compay ad 154 actvty lsted compaes the aalyss. Ths paper select sample lsted compaes from 2007 to 2009 for forecastg sample. It radomly selected 46 facally dstressed compay ad 128 actvty lsted compaes the aalyss as forecastg samples. 5.3 Reduced the umber of facal rato There are two ways to reduce the large umber of facal rato (1) Pearso correlato (2) The model accepted has a good ft ad that the mult-learty level s acceptable. Accordg to Pearso correlato, the correlato betwee CUR ad QUK s , whch are statstcally sgfcat wth p-value less tha Ths meas the postve relatoshp 111

10 betwee these par of varable. Based o the lkelhood rato resulted from Pearso correlato, the covarates QUK are selected to Cox proportoal hazards model. Table 4 s the Cox proportoal hazards model. Table 4: The Cox proportoal hazards model Varable D F Parameter Coeffcet Stadard error Chsquare pr> chsq Hazard Rato EBT ROE ** ROA ** QUK DET DER ** FAT ** CAT PSR PER PBV ** ** Sgfcat at 5 percet Usg Cox proportoal hazards model wth facal ratos, the proportoal hazards model are represeted Table 4. I SAS software, PROC RHREG s used to ft the Cox proporto hazards model ad to aalyze the effects of the facal o the survval of the compay. Table 4 s deoted as the coeffcet estmato, the Stadard error, Ch-square tests wth the relatve p-value for testg the ull hypothess that the coeffcet of each covarate s equal to zero. Hazard rato s obtaed by computg e, where s the coeffcet a proportoal hazard model. By cosderg the p-value, sx covarates are hghly sgfcat at 5 percet. These ratos are EBT, QUK, DET, CAT, PSR ad PER wth the coeffcet , , , , ad respectvely. Therefore, the early warg dcators are ROE, ROA, DER, FAT ad PSV. ROE ad ROA are egatve value dcatg that a crease ether covarate decreases the hazard of eterg to facally dstressed. Hazard rato of ROE s ( e 0.769). It meas that a crease of oe ut ROE mples decreases rsk facal dstress. For the sample ths study, proftablty (EBT), lqudty (QUK), leverage (DET), Effcecy (CAT) ad Valuato (PSR, PER) have ever foud statstcally sgfcat the model. The model s show as follow: Log h t) ROE( t) ROA( t) DER( t) FAT ( t) PSV ( ) 5.4 Goodess-of-ft test ( t Oe measure of overall goodess-of-ft test s partal lkelhood-rato test. I SAS software, PROC RHREG s used to obta the lkelhood rato ch-square statstc from the model ft statstcs Table 5. I Table 5, the output produces cludes the value of -2log lkelhood for fttg, AIC (Akake Iformato Crtero) ad SBC (Schwartz Bayesa Crtero) for fttg a model wthout covarace ad fttg a model wth covarates. 112

11 Akake [2] troduced the cocept of the formato crtera as a tool optmal model selecto. AIC s a fucto of the umber of observatos, the sum of square errors (SSE), ad the umber of depedet varables k p 1 where k cludes the tercept, as show (17). SSE AIC l[ ] 2k (17) The frst term (17) s a measure of the model lack of the ft whle the secod ter (2k) s a pealty term for addtoal parameters model. Schwartz [51] derved from a Bayesa modfcato of the AIC crtero to develop a SBC model. SBC s a fucto of the umber of observatos, the SSE, ad the umber of depedet varables k p 1 where k cludes the tercept, as show (18). SSE SBC l[ ] k l (18) Table 5: Goodess-of-ft test Crtero -2 LOG L AIC SBC The PHREG Procedure Model Ft Statstcs Wthout Covarates Wth Covarates Testg Global Null Hypothess: Beta = 0 Test Ch-square DF Pr > ch-square Lkelhood Rato <0.001 Score <0.001 Wald <0.001 The ch-square of lkelhood rato s ( ). Ths statstc s also show the Table 5 Testg Global Null Hypothess: Beta = 0. The lkelhood-rato test, Score test ad Wald test equals , , respectvely, wth 4 degree of freedom. Thus, the ull hypothess s rejected (p<0.001). Aother measure of model performace may be some measure aalogous to R 2, as show the formula below. Keep the md that ths measure does ot expla the proporto of varablty of the respose varable by the explaatory varables as the lear regresso. 2 L(0) R 1 [ ] 2 N cs 1 exp[( L(0) L( )) * 2 / N ] = L( ) R 2 2 / max 2 N Rcs Rcs = R cs 2 2 /( 1 [ L(0)] ) =

12 The valdato by Cox & Shell R 2 ad Nagelkerke R 2 shows that the explaatory varables of the predcto model process explaatory power for the cdece of facal dstress. After we have settled o assessg the adequacy of the model that seems a good-ft, we ca carry out statstcal ferece of a ftted model. The output below s produced by rug PROC PHREG wth 5 covarates, ROE, ROA, DER, FAT ad PBV. The RL (RISKLIMTS) opto the Model statemet provdes 95% cofdece terval for the hazard rato estmates. Table 6 s the PHREG procedure. Varable D F Parameter Coeffcet Table 6 The PHREG Procedure Aalyss of Maxmum Lkelhood Estmates Stadard error Chsquare pr> chsq Hazard Rato 95% Hazard Rato Cofdece lmts ROE ** ROA ** DER ** FAT ** PBV ** ** Sgfcat at 5 percet Results of the aalyss dcate that fve covarates appear to add sgfcatly to the model. The p-value of the parameter estmates for the regresso coeffcets are hghly sgfcat for ROE, ROA, DER, FAT ad PBV. The coeffcet sgs of ROE, ROA DER covarates are egatve dcatg that a crease ether covarate decreases the hazard of eterg to facally dstressed. For example, Hazard rato of ROE covarate s ( e ). It meas that a crease of oe ut ROE covarate mples decreases rsk facal dstress. The terpretato of the estmated hazard rato of ROE s It meas that a crease of oe ut the rato of Net come to Total equty wll shrk the hazard rate by 23.1% ( ). The terpretato of the estmated hazard rato of (FAT) s that facal compaes ths study fal at about tmes the rate of those o-facal sector. The 95% cofdece terval for hazard rato suggests a sector as low as or as hgh as The terval wdth equals ( ). Ths terval also cludes the pot estmate of ad does ot cota the ull value of Accuraces of classfcato o the model The ft of PH model used ths study s valdated by comparg the predcted value of each sample wth the cutoff value [40]. If the predcted value s below ths cut value, the sample s classfes as a dstressed compay; otherwse, the compay s classfed as o-dstressed compay. Accordg to the suggesto of Mart [41], ths study uses emprcal cutoff value whch s the percetage of facal dstressed samples total sample at (46/174). The accuraces of classfcato of the model are compled Table

13 Table 7: The accuraces of classfcato of the mode No-dstressed No-dstressed compay Dstressed compay Accuracy of Classfcato Observed value No-dstressed compay /128 (89.84%) Dstressed compay / 46 (82.60%) Overall accuracy of classfcato 153/174 (87.93%) Therefore, Type Ⅰ error s 13 /128 = 10.64% ad Type Ⅱ error s 8 /46 =17.50 % ad the overall accuracy of classfcato s 87.93% 6. CONCLUSION I ths paper, the lsted compaes o the Tawa Stock Exchage that expereced data betwee 2003 ad 2009 are employed as dstressed data set. I order to better aalyze the effect of the Cox model predcted, ths study estmated that from 2003 to 2009 sample was dvded to estmatg samples ad forecastg samples. Ths paper selected 56 dstressed compaes ad 154 o-dstressed compaes for estmatg samples data betwee 2003 ad 2006; 46 dstressed compaes ad 128 o-dstressed compaes for forecastg samples data betwee 2007 ad Form the proposed steps of busess falure predcto model; the facal dstress probablty model s costructed usg Proftablty, Leverage, Effcecy ad Valuato rato varables. Step 1 select the facal ratos for usg the developmet of bakruptcy predcto model. Step 2 cosder the survval problem, the choce of lsted compaes lsted o the Tawa Stock Exchage usg aual data o facal ratos for the perod I Step 3, there are two ways to reduce the large umber of facal rato (1) Pearso correlato (2) The model accepted has a good ft ad that the mult-learty level s acceptable. I SAS software, PROC RHREG s used to ft the Cox proporto hazards model ad to aalyze the effects of the facal o the survval of the compay. Step 4, oe measure of overall goodess-of-ft test s partal lkelhoodrato test. I SAS software, PROC RHREG s used to obta the lkelhood rato ch-square statstc from the model ft statstcs. The valdato by Cox & Shell R 2 ad Nagelkerke R 2 shows that the explaatory varables of the predcto model process explaatory power for the cdece of facal dstress. I Step 5, cosder the robustess of model predcto accuracy, ths study the accuraces of classfcato of the mode overall accuracy of classfcato s 87.93%. ACKNOWLEDGEMENTS I would lke to thak the aoymous revewers for ther costructve commets o ths paper. 115

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17 programmg ad support vector mache. 4th Iteratoal Coferece o Natural Computato, IEEE Computer Socety, 2008, pp [72] Zhao, H, (2007), A mult-objectve geetc programmg approach to developg Pareto optmal decso tree. Decso Support Systems, Vol. 43, No. 3, pp [73] Zhou, J. ad Ba, T., (2008), Credt rsk assessmet usg rough set theory ad GA-based SVM. The 3rd Iteratoal Coferece o Grd ad Pervasve Computg- Workshops, IEEE Computer Socety Kumg, 2008, pp [74] Zhou, L. ad La, K. K. ad Yu, L.,(2009), Credt scorg usg support vector mache wth drect search for parameters selecto. Soft Computg, Vol. 13, No. 2, pp [75] Zhou, L., La, K. K., ad Yu, L.,(2010), Least squares support vector maches esemble models for credt scorg. Expert Systems wth Applcatos, Vol. 37, No. 1, pp [76] Zulkarma, M. S., Mohamad, A. A. H., Auar, M. N. ad Zaal, A. M. (2001), Forecastg corporate falure Malaysa dustral sector frms. Asa Acdemy of Maagemet Joural, Vol. 6, No.1, pp [77] Buyamu, A. ad Bashru, S. (2014), Corporate falure predcto: A fresh techque for dealg effectvely wth ormalty based o quattatve ad qualtatve approach, Iteratoal Joural of Facal Ecoomc, Vol. 3, No. 1, pp Author Mg-Chag Lee s Assstat Professor at Natoal Kaohsug Uversty of Appled Sceces. Hs qualfcatos clude a Master degree appled Mathematcs from Natoal Tsg Hua Uversty ad a PhD degree Idustral Maagemet from Natoal Cheg Kug Uversty. Hs research terests clude kowledge maagemet, parallel computg, ad data aalyss. Hs publcatos clude artcles the joural of Computer & Mathematcs wth Applcatos, Iteratoal Joural of Operato Research, Computers & Egeerg, Amerca Joural of Appled Scece ad Computers, Idustral Egeerg, Iteratoal Joural ovato ad Learg, It. J. Servces ad Stadards, Lecture Notes computer Scece (LNCS), Iteratoal Joural of Computer Scece ad Network Securty, Joural of Covergece Iformato Techology ad Iteratoal Joural of Advacemets computg Techology. 119