ISSN 1822-8011 (p in )
ISSN 1822-8038 (online)
INTELEKTINĖ EKONOMIKA
INTELLECTUAL ECONOMICS
2013, Vol. 7, No. 3(17), p. 333–343
DEFAULT PREDICTION OF SPANISH COMPANIES.
A LOGISTIC ANALYSIS
Concepción BARTUAL
Uni e si a Poli ècnica de València
E-mail: conba [email protected] .es
Fe nando GARCIA
Uni e si a Poli ècnica de València
E-mail: e ga [email protected] .es
F ancisco GUIJARRO
Uni e si a Poli ècnica de València
E-mail: [email protected] .es.
Ismael MOYA
Uni e si a Poli ècnica de València
E-mail: [email protected] .es
doi:10.13165/IE-13-7-3-05
Abs ac . In he ield o c edi isk managemen , he calcula ion o he p obabili y o
de aul o companies plays a key ole. Fo ha eason, bank up cy p edic ion o companies has
gene a ed ex ensi e esea ch in he pas decades. This pape applies one o he mos popula
echniques, he logis ic eg ession. This echnique is ex ensi ely used bo h by p o essionals
and academics and is employed in many s udies as a benchma k. He e we will apply i on
a as da a base o he Spanish companies and a s a is ical analysis o he obus ness o he
model will be unde aken, wi h e y sa is ac o y esul s.
JEL classi ica ion: G32, G33.
Keywo ds: Logi model, isk managemen , bank up cy p edic ion.
Reikšminiai žodžiai: logis inis modelis, izikos aldymas, bank o o p ognoza imas.
In oduc ion
C edi isk analysis is one o he mos impo an asks o be unde aken by inan-
cial ins i u ions. The lack o a co ec me hodology o calcula e he p obabili y o de aul
o he clien s may lead o high losses in he banks, c ea e sys emic isk, and a ec he
whole economy o a coun y. An example o such an e en can be seen in he Spanish
334 Concepción Ba ual, Fe nando Ga Cía, F ancisco Guija o, F ancisco Guija o
case, whe e he economy is su e ing because o he high de aul a es o he c edi s
and he huge losses o he c edi ins i u ions om 2010. I has become ob ious ha he
c edi isk managemen unde aken by he Spanish banks in he p e ious decade has
been inadequa e.
Fo ecas ing bank up cy isk o en e p ises is one o he i s uses gi en o inancial
accoun ing in o ma ion. In ac , he s udy o he i ms’ p obabili y o de aul and he
de elopmen o c edi a ings had al eady gained ele ance in 1909, when he US a ing
agencies s a ed analysing he inancial si ua ion o he ailway companies. Ne e heless,
he o igin o he bank up cy p edic ion models lies in he 1960’s decade. Bea e (1966)
showed using 30 accoun ing a ios ha he alue o some o hose a ios a ied signi i-
can ly be ween dis essed and non-dis essed companies. Fu he mo e, Al man (1968)
applied disc iminan analysis on se e al inancial a ios in a mul i a ia e con ex and
gene a ed a model o p edic business ailu e. Tha was he s a ing poin o a ield o
esea ch ha has become inc easingly impo an , whe e new, mo e accu a e, p edic ion
models wi h new me hodologies and bigge da a bases a e s ill de eloped.
Many echniques ha e been used a e he s udies by Bea e (1966) and Al man
(1968) o p edic co po a e inancial dis ess employing he economic and inancial in-
o ma ion om he accoun ing sys em.
Following Ra i Kuma and Ra i (2007), he me hods used o analyse co po a e c e-
di isk can be di ided in o wo big g oups: s a is ical me hods and a i icial in elligence
echniques. The quan i y o s udies unde aken in his ield is eno mous, which is a p oo
o how impo an i ac ually is in he p esen imes o manage c edi isk app op ia ely,
and he in e es showed by academics and p ac i ione s.
Wi hou being exhaus i e, we can e e o he ollowing me hodologies and ech-
niques: some o he mos widesp ead s a is ical me hods a e disc iminan analysis (Yim
and Mi chell, 2004); he p obi model (Ginoglou and Ago as os, 2002) and he logis ic
eg ession (Ohlson, 1980), which is he one o be applied in his s udy. The e o e, we
will commen on i la e . Wi hin he a i icial in elligence echniques we can coun neu-
onal ne wo ks (Ra i and P amodh, 2008), decision ees (Ko ol, 2013), ough se s (Tay
and Shen, 2002; McKee, 2003), da a en elopmen analyses (Cielen e al., 2004), suppo
ec o machines (Kim and Sohn, 2010) and gene ic algo i hms (E emadi e al., 2009),
and goal p og amming (Ga cía e al. 2013) a e he mos common ones and some ecen
wo ks.
Al hough many new echniques ha e been applied in he las yea s o p edic com-
panies’ dis ess, he logi model is s ill widely accep ed among esea che s and p ac i-
ione s. Some o he mos p es igious a ing agencies use logi models o gene a e hei
company classi ica ions. And many ecen academic esea ches apply he logis ic eg es-
sion o p edic co po a e de aul (Joo-Ha and Taehong, 2000; Kola i e al., 2002; Lin
and Piesse, 2004; Jones and Henshe , 2004; Canbas e al., 2005; Chen and Zhang, 2006;
Al man and Saba o, 2007; Pang-Tien e al. 2008; Psillaki e al., 2010; He nández and
Wilson, 2013; Zaghdoudi, 2013) o as a benchma k o compa e he new c edi isk p e-
dic ion me hods (Min and Jeong, 2009; Kim and Sohn, 2010; Su and Huang, 2010; Chen,
2011; Li e al., 2011; Chaudhu i, 2013). One o he bigges challenges aced by esea che s
when applying he logis ic eg ession is o bene i om a la ge and comp ehensi e da a
335
De aul P edic ion o Spanish Companies. a Logis ic Analysis
base wi h high quali y accoun ing in o ma ion ha gua an ees o he obus ness o he
model ob ained and he accu acy o he p edic ions (Ba ual e al., 2012a).
Howe e , one mus be awa e o ce ain obus ness p oblems ha may a ise when
using logi , especially in ela ion o he composi ion o he sample used o es ima e he
model. Resea che s should pay close a en ion o h ee ac o s: he choice o a iables
o be used in he model, he in luence o he sample on he model esul s and he cu o
poin .Wha e e he a iables used, he logi model inally ob ained will depend on he
sample on which he model is based. This means ha only some o he p eselec ed a ia-
bles will ac ually be used in he model, since bo h he selec ion and he weigh ing o he
a iables will depend on he sample o companies.
Fu he mo e, wha e e he chosen cu o poin , e en hough i will no modi y
nei he he selec ed a iables no hei weigh s, his cu o poin will a ec he disc imi-
na ion p ocess and hus also he pe cen age o co ec and inco ec p edic ions.
The aim o he p esen s udy is o ob ain a model o p edic co po a e de aul o he
Spanish manu ac u ing companies applying he logis ic eg ession model. The goal is o
help sol ing an impo an issue in he Spanish economy, imme sed as i is in a p o ound
economic and inancial c isis. No only inancial ins i u ions, bu also clien s, supplie s,
he public adminis a ion and o he economic agen s a e in he need o know he p o-
babili y o de aul o he companies wi h which hey in e ac . In o de o cons uc he
model, a da abase has been c ea ed wi h he accoun ing in o ma ion om mo e han
2,000 companies o he yea 2010. A ha yea , he e ec s o he inancial c isis eme ged
and many i ms we e nega i ely a ec ed. I is a la ge da abase, much bigge han he
ones used in simila wo ks, which makes i possible o ob ain a obus model capable o
accu a e p edic ions.
The emainde o he pape is s uc u ed as ollows. Sec ion 2 desc ibes he da a-
base and he selec ed explana o y a iables. Sec ion 3 p esen s he main esul s and he
sensi i i y analyses. Finally, sec ion 4 is de o ed o he conclusions.
1. Desc ip ion o he Da abase and he Selec ed Explana o y Va iables
In his sec ion, he da abase employed is p esen ed. The selec ion o he g oup o
companies o analyse and he quali y and e aci y o he inancial in o ma ion employed
a e c i ical s eps owa ds ob aining a obus model. Fu he mo e, in o de o implemen
he sensibili y analysis i is necessa y o coun wi h a high numbe o da a. Finally, i is
impo an o include in he da abase an ele a e amoun o de aul ed companies. In ac ,
i he numbe o dis essed companies in he subsamples we e oo low, a solu ion s a ing
ha all companies a e sol en would be e y di icul o bea .
A e aking all o hese ac o s in o conside a ion, he da abase SABI-In o ma was
consul ed. This da abase has go accoun ing and inancial in o ma ion o almos all non-
inancial i ms in Spain, supplied by he companies hemsel es. In o de o gua an ee he
e aci y and accu acy o he in o ma ion and o wo k wi h a homogeneous sample o
companies, only i ms wi h accoun ing in o ma ion o 2010 we e conside ed. This yea
336 Concepción Ba ual, Fe nando Ga Cía, F ancisco Guija o, F ancisco Guija o
was chosen because i was he i s one in which he Spanish economy el he impac o
he inancial c isis, inc easing he numbe o de aul ed companies. I is no ewo hy o
men ion ha in he p eceden yea s he bank up i ms wi hin he selec ed sample we e
almos inexis en , making any co po a e dis ess p edic ion analysis i ually impossible.
Ou o he 2,783 selec ed companies, 736 we e iden i ied as insol en (26.5% o he
sample). A i m is classi ied as being in inancial dis ess when i s ne wo h is nega i e
o has o mally de aul ed on i s obliga ions, ha is, when i s legal s a us is de ined as
suspended o in liquida ion. Among he 736 companies ha ailed, 251 had a nega i e
equi y alue and he emaining 485 companies had o mally de aul ed.
The a iables employed in he sol ency analysis we e ob ained om he balance
shee s and he income s a emen s o he companies: o al asse s, cu en asse s, cash,
equi y, cu en liabili ies, o al sales, cos o aw ma e ials, labou cos s, ope a ing in-
come, inancial income and p e- ax p o i s. Using hese 11 accoun ing inpu s, se e al
inancial a ios we e calcula ed:
1. ET: Equi y / To al asse s
2. CL: Cash / Cu en liabili ies
3. LS: Labou cos s / Sales
4. OS: Ope a ing income / Sales
5. OT: Ope a ing income / To al asse s
Al oge he , 16 explana o y a iables we e used o ob ain he co po a e de aul p e-
dic ion model. The selec ion o he a iables was unde aken ollowing Ba ual e al., 2012 b.
Summa y s a is ics o explana o y inancial and a io a iables can be ound in Table 1.
Table 1. Desc ip i e s a is ics
Va iable Minimum Maximum Mean Median S anda d de ia ion
To al asse s 11 3,065,534 6,339.8 687 76,298.0
Cu en asse s 2 1,749,916 3,205.0 391 36,195.9
Cash 0 33,991 183.9 28 1,021.2
Equi y -26,264 873,721 2,186.4 150 24,734.9
Cu en liabili ies 1 392,810 2,095.2 288 13,422.2
To al sales 5 1,476,753 4,922.0 640 40,729.6
Cos o aw ma e ials 0 873,897 2,954.2 286 25,195.9
Labo cos s 0 125,211 814.2 210 4,122.3
Ope a ing income -26,019 285,172 153.1 6 6,394.7
Financial income -42,043 22,769 -43.3 -6 1,033.8
P e- ax p o i s -18,244 873,897 2,954.2 286 5,161.0
ET -16.657 0.998 0.231 0.266 0.659
CL 0.000 105.000 0.511 0.087 3.020
LS 0.000 15.571 0.404 0.331 0.641
OS -37.000 33.862 -0.131 0.013 1.323
OT -39.363 0.956 -0.077 0.013 0.807
No e: Balance shee and income accoun s a e exp essed in housands o eu os.
Sou ce: The au ho s.
337
De aul P edic ion o Spanish Companies. a Logis ic Analysis
The p oposed logi model makes i possible o es ima e he likelihood o a i m o
belong o he g oup o sol en companies (i he ob ained alue is 1) o o he g oup o
insol en companies (i he alue is 0) using he 16 independen a iables in oduced
abo e. In o de o iden i y he mos signi ican and obus model, he s epwise me hod
has been applied and op imised by he Akaike index (AIC). The selec ed model is p e-
sen ed in Table 2.
Table 2. Resul o he s epwise logis ic eg ession
Es ima e S d. E o z alue P (>|z|)
(In e cep ) 3.837e-01 8.698e-02 4.411 1.03e-05 ***
Cu en asse s -1.842e-04 5.047e-05 -3.649 0.000263 ***
Equi y 1.577e-04 5.179e-05 3.046 0.002320 **
Cu en liabili ies 1.764e-04 4.920e-05 3.585 0.000337 ***
Financial income 1.648e-03 4.108e-04 4.011 6.06e-05 ***
P e- ax p o i s 8.911e-04 1.832e-04 4.864 1.15e-06 ***
Equi y / To al asse s 5.281e+00 3.222e-01 16.391 < 2e-16 ***
Cash / Cu en liabili ies 8.275e-01 2.184e-01 3.790 0.000151 ***
Ope a ing income / To al asse s 5.910e+00 5.226e-01 11.309 < 2e-16 ***
Signi . codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispe sion pa ame e o binomial amily aken o be 1)
Null de iance: 3219.4 on 2782 deg ees o eedom
Residual de iance: 1632.7 on 2774 deg ees o eedom
AIC: 1650.7
Numbe o Fishe Sco ing i e a ions: 9
Sou ce: The au ho s.
The p ocess has con e ged a e 9 i e a ions and he coe icien s o ollowing expla-
na o y a iables a e signi ican wi h a le el o con idence o 99%: Cu en asse s, equi y,
cu en liabili ies, inancial esul , p e- ax p o i s, equi y / o al asse s, cash / cu en liabi-
li ies, y ope a ing income / o al asse s. The alue ob ained by he Akaike index is 1,650.7.
I is possible o d aw some in e es ing conclusions by simply looking a he sign o
he coe icien s. The coe icien wi h he highes z- alue is he one o he a io equi y /
o al asse s, wi h a posi i e sign. This is due o he impo ance o ha ing an ele a e equi y
alue compa ed wi h he liabili ies, ha is, ha ing a educed inancial le e age, in o de
o a oid bank up cy. The second coe icien wi h he highes z- alue, ha ing a posi i e
sign as well, is he a io ope a ing income / o al asse s. This unde lines he necessi y o
ha ing high bene i s compa ed wi h he size o he i m o gua an ee he su i al o any
company. The a io cash / cu en liabili ies is ema kable as well. I s posi i e sign shows
ha i is impe a i e o he companies o ha e enough cash o pay he money back o
c edi o s and se le he deb s. I his condi ion is no me , he company will be h ea ened
wi h insol ency. The emaining a iables ha e he coe icien s ha sha e a simila econo-
mic in e p e a ion as he a iables commen ed abo e.
When he model is applied on he o al da abase, he esul s shown on Table 3
a e ob ained. Ou o he 738 de aul ed co po a ions, he model co ec ly p edic s he

338 Concepción Ba ual, Fe nando Ga Cía, F ancisco Guija o, F ancisco Guija o
si ua ion o 573 (77.6%). The es (22.4%) is inco ec ly assigned o he g oup o sol en
companies. In he case o he sol en companies, ou o he 2,045 i ms, 1,880 a e co -
ec ly de ined as sol en (91.9%), whe eas only 165 (8.1%) a e w ongly p edic ed o be
in bank up cy.
I he o al numbe o companies in he sample is o be conside ed ega dless hei
sol ency / insol ency s a e, he model can co ec ly assess he c edi isk in 88.1% o he
cases. A naï e model would p edic ha all he i ms a e sol en 1, ob aining a success a e
o 73.5%; equal o he pe cen age o sol en i ms in he sample. The e o e we can con-
i m ha ou model bea s by almos 15% he esul s ob ained by he naï e model. This
pe o mance o ou model can be conside ed as a good esul .
Table 3. Sol ency s a e p edic ion applying he logis ic eg ession model
Obse ed sol ency P edic ed sol ency
0 1 Row To al
0
573 165 738
727.386 262.499
0.776 0.224 0.265
0.776 0.081
0.206 0.059
1
165 1880 2045
262.499 94.731
0.081 0.919 0.735
0.224 0.919
0.059 0.676
Column To al 738 2045 2783
0.265 0.735
Sou ce: The au ho s.
2. Resul s and Sensi i i y Analyses
The esul s o e ed in he p e ious sec ion clea ly indica e he kind o accoun ing
a iables ha can be included in a model o he p edic ion o co po a e insol ency in
Spain. They also show he success a e o he model o each o he g oups in o which
he sample was di ided: sol en and insol en i ms. The a e age success a e is 88.1%.
Ne e heless, he analysis migh be biased as he same sample has been employed o he
es ima ion o he model and o he p edic ion o he dependen a iable.
In o de o a oid his kind o bias, he comple e simple has been di ided in o wo
subsamples, he i s one including 80% o he companies and he second one he emai-
ning 20%. The i s , bigge subsample has been employed as aining se o es ima e he
1 A nai e model conside s all he i ms o be sol en . So, i he e a e 90% o sol en i ms in he
sample, he naï e model would make co ec p edic ions in 90% o he cases. Bu all insol en
i ms would be w ongly assigned o he g oup o sol en companies.
339
De aul P edic ion o Spanish Companies. a Logis ic Analysis
p edic ion model. The second sample is he es se . The model ob ained using he big
subsample is applied on he es se and he a e o success is calcula ed.
Fu he mo e, his p ocess has been simula ed 1,000 imes by andomly selec ing
he companies o be assigned o he aining se and o he es se . Doing his, he model
ob ained in each simula ion is sligh ly di e en , and so was he a e o success.
Figu e 1 ep esen s he his og am o he a iable “success a e”. This a iable shows
he pe cen age o companies belonging o he se es o which hei sol ency / insol en-
cy es a e was co ec ly p edic ed. We can obse e ha he dis ibu ion o his a iable is
simila o he no mal dis ibu ion, wi h a mean alue o 87.96% and a s anda d de ia-
ion o 0.01479. Clea ly, he success a e ob ained o he comple e sample o companies
(88.1%) can be conside ed o be wi hin he ange ob ained o he mean success a e wi h
a con idence le el o 99%.
In conclusion, once he simula ion p ocess is unde aken, i becomes ob ious ha
he logi model is a obus me hodology o p edic co po a e de aul and ha a high
success a e migh be expec ed (88.1%) o he case o he Spanish manu ac u ing com-
panies when using he s anda d accoun ing a iables.
Figu e 1. His og am o he a iable “success a e”
Sou ce: The au ho s.
Conclusion
The p esen wo k shows he applica ion o a mul i a ia e s a is ical model, he logi
model, o p edic co po a e dis ess. As p edic i e a iables, commonly-used accoun-
ing in o ma ion has been used om a da abase including 2,783 Spanish manu ac u ing
i ms.
340 Concepción Ba ual, Fe nando Ga Cía, F ancisco Guija o, F ancisco Guija o
In ou sample, 73.5% o he i ms a e sol en , while 26.5% ha e been de ined as
de aul ed. The logi model ob ained combines in o ma ion ob ained om he balance
shee and om he income s a emen o he companies, which has been used in o de o
calcula e se e al economic and inancial a ios. When he model is applied on he com-
ple e sample, we ob ain a co ec p edic ion o he sol ency/insol ency o he companies
in 88.1% o he cases. The e o e, we can s a e ha he logi model bea s he esul ha
would be ob ained by a naï e model, which would be a success a e o only 73.5%.
Wi h he aim o a oiding he bias ha can appea when he same simple is used
o gene a e he model and o calcula e he a e o success, 1,000 simula ions ha e been
calcula ed. In he simula ions, 80% o he companies o he sample we e andomly as-
signed o he aining se and he emaining 20% o he companies o he es se . The
esul s make e iden ha he logi model is a obus me hodology o explain and p edic
co po a e bank up cy.
Fo u u e lines o esea ch we can p opose he use o o he echniques om he
a i icial in elligence ield o be compa ed wi h he logi model, which is he adi ional
benchma k o c edi isk e alua ion. Such echniques include neu onal ne wo ks, and
suppo ec o machines. The compa ison o he logi model applied in he p esen s udy
and hese al e na i e me hodologies will p obably e eal in e es ing di e ences ega -
ding he numbe o independen a iables in he models and he a e o success.
Re e ences
1. Al man, E. (1968) Financial a ios, disc iminan analysis and he p edic ion o co -
po a e bank up cy. Jou nal o Finance, 23. 589-609.
2. Al man, E., Saba o, G. (2007) Modelling isk o SMEs –e idence om US ma ke .
Abacus 43 (3), 332-356.
3. Bea e , W. (1966) Financial a ios as p edic o s o ailu e. Jou nal o Accoun ing
Resea ch, 4, 71-111.
4. Ba ual. C., Ga cía, F., Giménez, V., Rome o, A. (2012a) C edi isk analysis: Re -
lec ions on he use o he logi model. Jou nal o Applied Finance and Banking 2(6),
1-13.
5. Ba ual, C., Ga cía, F., Guija o, F., Rome o-Ci e a, A. (2012b) P obabili y o de-
aul using he logi model: The impac o explana o y a iable and da a base selec-
ion. 2nd In e na ional Scien i ic Con e ence Whi he Ou Economies. Con e ence
P oceedings. Mykolas Rome is Uni e si y.
6. Canbas, S., Cabuk, A., Kilic, S. B. (2005) P edic ion o come cial bank ailu e ia
mul i a ia e s a is ical analysis o inancial s uc u e: The Tu kish case. Eu opean
Jou nal o Ope a ional Resea ch 166, 528-546.
7. Chaudhu i, A. (2013) Bank up cy p edic ion using bayesian, haza d, mixed logi
and ough Bayesian models: A compa a i e analysis. Compu e and In o ma ion
Science, 6, 103-125.
8. Chen, J., Zhang, J. (2006) Financial dis ess p edic ion in China. Re iew o Paci ic
Basin Financial Ma ke s and Policies, 9 (2), 317-336.
341
De aul P edic ion o Spanish Companies. a Logis ic Analysis
9. Chen, M. Y. (2011) P edic ing co po a e inancial dis ess based on in eg a ion o
decision ee classi ica ion and logis ic eg ession. Expe Sys ems wi h Applica ions,
38, 11261-11272.
10. Cielen, A., Pee e s, L., Vanhoo , K. (2004) Bank up cy p edic ion using a da a en elop-
men analysis. Eu opean Jou nal o Ope a ional Resea ch, 154, 526-532.
11. E emadi, H., Ros amy, A., Dehko di, H. (2009) A gene ic p og amming model o
bank up cy p edic ion: Empi ical e idence om I an. Expe Sys ems wi h Applic-
a ions, 36 (2), 3199-3207.
12. Ga cía, F., Giménez, V., Guija o, F. (2013) C edi isk managemen : A mul ic i e-
ia app oach o assess c edi wo hiness. Ma hema ical and Compu e Modelling, 57,
2009-2015.
13. Ginoglou, D., Ago as os, K. (2002) P edic ing co po a e ailu e o p oblema ic i ms
in G eece wi h LPM, logi , p obi and disc iminan analysis models. Jou nal o
Financial Managemen and Analysis, 15 (1), 1-15.
14. He nández, M., Wilson, N. (2013) Financial dis ess and bank up cy p edic ion
among lis ed companies using accoun ing, ma ke and mac oeconomic a iables.
In e na ional Re iew o Financial Analysis.
15. Jones, S., Henshe , D. A. (2004) P edic ing i m inancial dis ess: A mixed logi
model. Acoun ing Re iew 79 (4), 1011-1038.
16. Joo-Ha, N. Taehong, J. (2000) Bank up cy p edic ion- e idence om Ko ea lis ed
companies du ing he IMF c isis. Jou nal o In e na ional Financial Managemen
and Accoun ing, 11 (3), 178-197.
17. Kim, H. S., Sohn, S. Y. (2010) Suppo ec o machines o de aul p edic ion o SMEs
based on echnology c edi . Eu opean Jou nal o Ope a ional Resea ch, 201, 838-846.
18. Kola i, J., Glennon, D., Shin, H., Capu o, M. (2002) P edic ing la ge US comme cial
bank ailu es. Jou nal o Economics and Business 54 (32), 318-324.
19. Ko ol, T. (2013) Ea ly wa ning models agains bank up cy isk o Cen al Eu opean
and La in Ame ican en e p ises. Economic Modelling, 31, 22-30.
20. Li, H., Adeli, H., Sun, J., Han, J.G. (2011) Hyb idizing p inciples o TOPSIS wi h
case-based easoning o business ailu e p edic ion. Compu e s and Ope a ions
Resea ch, 38, 409-419.
21. Lin, L., Piesse, J. (2004) Iden i ica ion o co po a e dis ess in UK indus ials – a condi-
ional p obabili y analysis app oach. Jou nal o Applied Financial Economics, 14. 73-82.
22. McKee, T. E. (2003) Rough se s bank up cy p edic ion models e sus audi o signal-
izing a es. Jou nal o Fo ecas ing, 22, 569-589.
23. Min, J. H., Jeong, C. (2009) A bina y classi ica ion me hod o bank up cy p edic-
ion. Expe Sys ems wi h Applica ions, 36, 5256-5263.
24. Ohlson, J. A. (1980) Financial a ios and he p obabilis ic p edic ion o bank up cy.
Jou nal o Accoun ing Resea ch, 109-131.
25. Pang-Tien, L., Chin-Wen, L., Hui-Fun, Y. (2008) Financial ea ly-wa ning models on
c oss-holding g oups. Jou nal o Indus ial Managemen and Da a Sys ems, 108 (8),
1060-1080.
26. Psillaki, M., Tsolas, I. E., Ma ga i is, D. (2010) E alua ion o c edi isk based on i m
pe o mance. Eu opean Jou nal o Ope a ional Resea ch, 201, 873-881.