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Expert Systems with Applications 36 (2009) 4075–4086
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Expert Systems with Applications
journal homepage: www.elsevier.com/locate/eswa
Using neural networks and data mining techniques for the financial distress
prediction model
Wei-Sen Chen *, Yin-Kuan Du
Industrial Technology Research Institute, #195, Sec. 4, Chung-Hsing Rd., Chutung 310, HsinChu, Taiwan, ROC
a r t i c l e
i n f o
Keywords:
Financial distress prediction model
Artificial neural network
Data mining
a b s t r a c t
The operating status of an enterprise is disclosed periodically in a financial statement. As a result, investors usually only get information about the financial distress a company may be in after the formal financial statement has been published. If company executives intentionally package financial statements with
the purpose of hiding the actual status of the company, then investors will have even less chance of
obtaining the real financial information. For example, a company can manipulate its current ratio by
up to 200% so that its liquidity deficiency will not show up as a financial distress in the short run. To
improve the accuracy of the financial distress prediction model, this paper adopted the operating rules
of the Taiwan stock exchange corporation (TSEC) which were violated by those companies that were subsequently stopped and suspended, as the range of the analysis of this research. In addition, this paper also
used financial ratios, other non-financial ratios, and factor analysis to extract adaptable variables. Moreover, the artificial neural network (ANN) and data mining (DM) techniques were used to construct the
financial distress prediction model. The empirical experiment with a total of 37 ratios and 68 listed companies as the initial samples obtained a satisfactory result, which testifies for the feasibility and validity
of our proposed methods for the financial distress prediction of listed companies.
This paper makes four critical contributions: (1) The more factor analysis we used, the less accuracy we
obtained by the ANN and DM approach. (2) The closer we get to the actual occurrence of financial distress, the higher the accuracy we obtain, with an 82.14% correct percentage for two seasons prior to
the occurrence of financial distress. (3) Our empirical results show that factor analysis increases the error
of classifying companies that are in a financial crisis as normal companies. (4) By developing a financial
distress prediction model, the ANN approach obtains better prediction accuracy than the DM clustering
approach. Therefore, this paper proposes that the artificial intelligent (AI) approach could be a more suitable methodology than traditional statistics for predicting the potential financial distress of a company.
Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved.
1. Introduction
In Taiwan, domestic and foreign capital markets have developed
rapidly in recent years, gradually giving people the idea of making
a financial investment. There are various financial investment
objects, such as stocks, futures, options, bond funds etc., and
investment stock is the most widely accepted in society. However,
capital markets are volatile, and most investors only know that a
company is in financial trouble after the financial statement of
the company has been made public. Therefore, forecasting
corporate financial distress plays an increasingly important role
in today’s society since it has a significant impact on lending decisions and the profitability of financial institutions. The ability to
make accurate bankruptcy predictions are of critical importance
* Corresponding author. Tel.: +886 3 5820100; fax: +886 3 5610616.
E-mail address: [email protected] (W.-S. Chen).
to various professionals, such as bank loan officers, creditors,
stockholders, bondholders, financial analysts, governmental officials, as well as the general public, as it provides them with timely
warnings (Ko & Lin, 2006).
Financial failure occurs when a firm suffers chronic and serious
losses or when the firm becomes insolvent with liabilities that are
disproportionate to its assets (Hua, Wang, Xu, Zhang, & Liang,
2007). Common causes and symptoms of financial failure include
lack of financial knowledge, failure to set capital plans, poor debt
management, inadequate protection against unforeseen events
and difficulties in adhering to proper operating discipline in the
financial market. The common assumption underlying bankruptcy
prediction is that a firm’s financial statements appropriately reflect
above characteristics. Several classification techniques have been
suggested to predict financial distress using ratios and data
originating from these financial statements, e.g., univariate
approaches (Beaver, 1966), multivariate approaches, linear multiple
0957-4174/$ - see front matter Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2008.03.020
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W.-S. Chen, Y.-K. Du / Expert Systems with Applications 36 (2009) 4075–4086
discriminant approaches (MDA) (Altman, 1968; Altman, Edward,
Haldeman, & Narayanan, 1977), multiple regression (Meyer & Pifer,
1970), logistic regression (Dimitras, Zanakis, & Zopounidis, 1996),
factor analysis (Blum, 1974), and stepwise (Laitinen & Laitinen,
2000). However, strict assumptions of traditional statistics such as
linearity, normality, independence among predictor variables and
pre-existing functional form relating to the criterion variable and
the predictor variable limit their application in the real world
(Hua et al., 2007).
With radical changes taking place in corporate finance and the
global economic environment, critical financial ratios can change
dynamically (John & Robert, 2001). This means that it is both
important as well as necessary to develop an evolutionary approach for coping with future dynamic financial environments.
Therefore, this paper proposes a model of financial distress prediction integrating artificial neural network (ANN) and data mining
(DM) techniques. The main objectives of this paper are to (1) adopt
ANN and DM techniques to construct a financial distress prediction
model, (2) use financial and non-financial ratios to enhance the
accuracy of the financial distress prediction model, (3) employ a
traditional statistical method (factor analysis) to compare the degree of accuracy with that of the artificial intelligent (AI) approach,
and (4) to expand this model so that it will work within a financial
distress prediction system to provide information to investors as
well as investment monitoring organizations. The data for our
experiment were collected from the Taiwan stock exchange corporation (TSEC) database.
The rest of this paper is organized as follows. A literature review
of related studies is provided in Section 2. Section 3 describes our
proposed approach and the functionalities of each process. Section
4 presents the process for selecting suitable indicators by factor
analysis. To prove the prediction performance of our approach,
we carried out several experiments which are described in Section
5. In Section 6, we compared our results with the ANN, and DM approaches. Finally, in Section 7 we draw our conclusions about
financial distress forecasting and discuss future work.
2. Literature review
2.1. Artificial neural network
The ANN is composed of richly interconnected non-linear nodes
that communicate in parallel. The connection weights are modifiable, allowing ANN to learn directly from examples without requiring or providing an analytical solution to the problem. The most
popular forms of learning are:
niques for classification and prediction (Wu, Yang, & Liang, 2006),
and is considered an advanced multiple regression analysis that
can accommodate complex and non-linear data relationships (Jost,
1993). It was first described by Werbos (1974), and further developed by Ronald, Rumelhart, and Hinton (1986). The details for the
back-propagation learning algorithm can be found in Medsker and
Liebowitz (1994).
Fig. 1 shows the l m n (l denotes input neurons, mdenotes
hidden neurons, and n denotes output neurons) architecture of a
BPN model (Panda, Chakraborty, & Pal, 2007). The input layer can
be considered the model stimuli and the output layer the input
stimuli outcome. The hidden layer determines the mapping relationships between input and output layers, whereas the relationships between neurons are stored as weights of the connecting
links. The input signals are modified by the interconnection
weight, known as weight factor wji, which represents the interconnection of the ith node of the first layer to the jth node of the
second layer. The sum of the modified signals (total activation) is
then modified by a sigmoid transfer function (f). Similarly, the output signals of the hidden layer are modified by interconnection
weight wkj of the kth node of the output layer to the j th node of
the hidden layer. The sum of the modified signals is then modified
by sigmoid transfer (f) function and the output is collected at the
output layer.
Let Ip = (Ip1,Ip2, . . . , Ipl), p = 1,2, . . . , N be the pth pattern among N
input patterns. Where wji and wkj are connection weights between
the ith input neuron to the jth hidden neuron, and the jth
hidden neuron to the kth output neuron, respectively (Panda
et al., 2007).
Output from a neuron in the input layer is
Opi ¼ Ipi ;
i ¼ 1; 2; . . . ; l
Output from a neuron in the hidden layer is
!
1
X
Opj ¼ f ðNET pj Þ ¼ f
wji opi ; j ¼ 1; 2; . . . ; m
ð2Þ
i¼0
Output from a neuron in the output layer is
!
m
X
Opk ¼ f ðNET pk Þ ¼ f
wkj opj ; k ¼ 1; 2; . . . ; n
ð3Þ
j¼0
Where f( ) is the sigmoid transfer function given by f(x) = 1/(1 + ex).
BPN has been applied to various areas, such as investigating
long-term tidal predictions (Lee, 2004), improving customer satisfaction (Deng, Chen, & Pei, 2007), predicting flank wear in drills
(Panda et al., 2007), enhancing job completion time prediction in
the semiconductor fabrication factory (Chen, 2007), and providing
Supervised learning: Patterns for which both their inputs and
outputs are known are presented to the ANN. The task of the
supervised learner is to predict the value of the function for
any valid input object after having seen a number of training
examples. ANN employing supervised learning has been widely
utilized for the solution of function approximation and classification problems.
Unsupervised learning: Patterns are presented to the ANN in the
form of feature values. It is distinguished from supervised learning by the fact that there is no a priori output. ANN employing
unsupervised learning has been successfully employed for data
mining and classification tasks. The self-organizing map (SOM)
and adaptive resonance theory (ART) constitutes the most popular exemplar of this class.
A back-propagation network (BPN) is a neural network that
uses a supervised learning method and feed-forward architecture.
A BPN is one of the most frequently utilized neural network tech-
ð1Þ
Fig. 1. Back-propagation network architecture.
W.-S. Chen, Y.-K. Du / Expert Systems with Applications 36 (2009) 4075–4086
the required accuracy for focal ventricular arrhythmias diagnosis
(Yılmaz & Cunedioglu, 2007).
Based on the above literatures, many researches employed the
BPN techniques for many applications. However, few of them used
it to carry out empirical investigations of financial distress prediction related topics. Therefore, in this study we will use the BPN
technique to forecast a potential crisis in the bankruptcy prediction
domain. We hope that the results of our proposed approach will
provide a useful methodology for investors as well as supervisory
organizations to predict and avoid investing in, a company open
to a bankruptcy in the near future.
2.2. Data mining
Data mining (DM), also known as ‘‘knowledge discovery in databases” (KDD), is the process of discovering meaningful patterns in
huge databases (Han & Kamber, 2001). In addition, it is also an
application that can provide significant competitive advantages
for making the right decision. (Huang, Chen, & Lee, 2007). DM is
an explorative and complicated process involving multiple iterative steps. Fig. 2 shows an overview of the data mining process
(Han & Kamber, 2001). It is interactive and iterative, involving
the following steps:
Step 1. Application domain identification: Investigate and understand the application domain and the relevant prior knowledge.
In addition, identify the goal of the KDD from the administrators’
or users’ point of view.
Step 2. Target dataset selection: Select a suitable dataset, or
focus on a subset of variables or data samples where data
relevant to the analysis task are retrieved from the
database.
Step 3. Data Preprocessing: the DM basic operations include
‘data clean’ and ‘data reduction’: In the ‘data clean’ process, we
remove the noise data, or respond to the missing data field. In
the ‘data reduction’ process, we reduce the unnecessary dimensionality or adopt useful transformation methods. The primary
objective is to improve the effective number of variables under
consideration.
Step 4. Data mining: This is an essential process, where AI methods are applied in order to search for meaningful or desired patterns in a particular representational form, such as association
rule mining, classification trees, and clustering techniques.
Step 5. Knowledge Extraction: Based on the above steps it is possible to visualize the extracted patterns or visualize the data
depending on the extraction models. Besides, this process also
checks for or resolves any potential conflicts with previously
believed knowledge.
Step 6. Knowledge Application: Here, we apply the found knowledge directly into the current application domain or in other
fields for further action.
Step 7. Knowledge Evaluation: Here, we identify the most interesting patterns representing knowledge based data on some
measure of interest. Moreover, it allows us to improve the accuracy and efficiency of the mined knowledge.
A particular data mining algorithm is usually an instantiation of
the model preference search components. The more common model functions in the current data mining process include the following (Mitra, Pal, & Mitra, 2002).
Classification: Classifies a data item into one of several predefined categories.
Regression: Maps a data item to a real-valued prediction
variable.
Clustering: Maps a data item into a cluster, where clusters are
natural groupings of data items based on similarity metrics or
probability density models.
Association rules: Describes association relationship among different attributes.
Summarization: Provides a compact description for a subset of
data.
Dependency modeling: Describes significant dependencies
among variables.
Sequence analysis: Models sequential patterns, like time-series
analysis. The goal is to model the state of the process generating
the sequence or to extract and report deviations and trends over
time.
Knowledge
Evaluation
Knowledge
Applying
Knowledge
Extraction
Data Mining
Target
Dataset
Application Selection
Domain
Identification
4077
Data
Preprocessing
Fig. 2. Data mining phases (Han & Kamber, 2001).
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In the recent past many research contributions have applied
data mining techniques to many applications. DM has been successfully applied to several financial problem domains. Recent
examples are as follows. Huang, Hsu, and Wang (2007) adopted
the time-series mining approach to simulate human intelligence
and discover financial database patterns automatically (Huang
et al., 2007). Kirkos, Spathis, and Manolopoulos (2007) used classification mining to identify fraudulent financial statements (Kirkos
et al., 2007). Chun and Park (2006) integrated the regression analysis and case-based reasoning for predicting the stock market index (Chun & Park, 2006). However, few of these studies focused
on the data clustering approach, and even fewer empirical investigations were made of financial distress prediction related topics.
Therefore, we will use data clustering to enhance the accuracy of
predicting bankruptcy in a capital market.
3. Research methodology
In this study we integrate ANN and DM techniques for financial
distress prediction (FDP). The research methodology is as shown in
Fig. 3. In the first phase we deal with the dataset which basically is
the original huge set of records from the TSEC which will be covered by data pre-processing. The data sets then undergo cleaning
and preprocessing for removing discrepancies and inconsistencies
to improve their quality. The goal in this phase is to select the suitable indicators, including financial and non-financial ratios, by
means of factor analysis. After the above processes, the next phase
will load these indicators and discovery prediction rule sets that
are ready to be used in ANN and DM clustering. The ‘‘FDP Selecting” will be discussed in detail in the following sections.
In the FDP Modeling phase we collect the financial statement
data sets for ANN and DM processing. In the ANN approach, we will
use the BPN algorithm to discover the rules and predict the FDP. In
the DM approach, we will use the clustering technique to classify
and predict the FDP. Next, the selected data set is analyzed by
applying algorithms in order to identify the patterns among the
data that represent a relationship. The BPN and clustering algorithm are applied to separately determine the financial distress
prediction patterns or rules.
In the FDP Comparison phase, we compare the prediction accuracy for BPN and clustering mining by means of several times fac-
tor analysis (non-factor analysis, 1st factor analysis, and 2nd factor
analysis). Then, the intelligent financial distress prediction model
will be constructed and initiated to validate the new data sets of
the financial statement from the TSEC.
4. The FDP selecting phase
4.1. Data
Our sample contained data from 68 Taiwan firms listed in the
TSEC. The period of sampling was from 1999 January u/i October,
2006, amounting to 7 years and 10 months. The 34 firms in financial distress were matched with 34 non-bankruptcy firms. These
firms were characterized as non-bankruptcy based on the absence
of any indication or proof concerning the issuing of financial distress in the auditors’ reports, in the financial and taxation databases and in the TSEC. This of course did not guarantee that the
financial statements of these firms were not falsified or that the
financial distress of these firms would not be revealed in the future. It only guaranteed that no firms in financial distress had been
found during an extensive search. All the variables used in the
sample were extracted from formal financial statements, such as
balance sheets and income statements. This implies that the usefulness of this study is not restricted by the fact that only data from
Taiwanese companies was used.
4.2. Variables
The selection of variables to be used as candidates for participation in the input vector was based upon prior research work linked
to the topic of financial distress prediction. The work carried out by
Kirkos et al. (2007), Spathis (2002), Spathis, Doumpos, and Zopounidis (2002), Fanning and Cogger (1998), Persons (1995), Stice
(1991), Feroz, Park, and Pastena (1991), Loebbecke, Eining, and
Willingham (1989) and Kinney and McDaniel (1989) contained
the suggested indicators of financial distress prediction. Therefore,
this paper adopted the related variables based on prior researches,
the Taiwanese Economic Journal (TEJ), and the Taiwanese economic database. Moreover, this paper selected 37 variables and
categorized them as six major types: earning ability, financial
structure ability, management efficiency ability, management
Fig. 3. Research methodology.
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W.-S. Chen, Y.-K. Du / Expert Systems with Applications 36 (2009) 4075–4086
performance, debt-repaying ability, and non-financial factors. The
details of these indicators belong to each type and are listed as
follows:
Table 1
1st Factor analysis results
Factors
Variables
Factor
loadings
Communality
Eigenvalues
Explained
variance
Earning ability: Including pretax margin, return on total assets,
return on equity, earnings per share, and gross margin ratios.
Financial structure ability: Including debt to assets, times interest
earned, book value per share, financial leverage ratio, debt to
equity, short term and long term debt to book value ratio, fixed
assets to total assets ratio, gross margin to total assets ratio,
inventory to total assets ratio, inventory to sales ratio, investment ratio, and current assets to total assets ratios.
Management efficiency ability: Including turnover rate of inventory, turnover rate of account receivable, turnover rate of fixed
assets, turnover rate of total assets, turnover rate of equity,
and turnover rate of working capital ratios.
Management performance: Including pretax margin growth ratio,
gross margin growth ratio, and sales growth ratio ratios.
Debt-repaying ability: Including current ratio, acid-test ratio,
cash ratio, cash flow ratio, cash flow to long term debt, cash flow
to total debt, and cash flow to short term and long term debt
ratio ratios.
Non-financial factors: Including dividend payout ratio, pricebook ratio, the proportion of collateralized shares by the board
of directors, and the insider holding ratio.
1
Earnings per share
(EPS)
Return on equity
(ROE)
Return on asset
(ROA)
Pretax margin
growth ratio
Margin before
interest and tax
(BEFM)
0.870
0.919
4.023
10.874
0.862
0.889
0.850
0.866
0.641
0.524
0.638
0.814
2
Current ratio
Acid-test ratio
Equity per share
Cash ratio
Gross margin ratio
Price-book ratio
(PBR)
0.762
0.742
0.631
0.624
0.609
0.352
0.877
0.833
0.742
0.503
0.660
0.462
3.858
10.428
3
Gearing ratio
Debt to equity ratio
(DEBE)
Debt/equity (DE)
Debt ratio
0.949
0.948
0.969
0.968
3.738
10.103
0.923
0.625
0.962
0.820
Turnover rate of
total assets
Turnover rate of
equity
Turnover rate of
fixed assets
Gross margin to
total assets ratio
0.858
0.824
2.886
7.800
0.798
0.793
0.635
0.803
0.479
0.716
Inventory to total
assets ratio
Inventory to sales
ratio
Current assets to
total assets
The proportion of
collateralized
shares by the broad
of directors
0.899
0.889
2.558
6.912
0.848
0.802
0.578
0.871
0.422
0.397
Cash flow ratio
Cash flow to total
debt ratio
Dividend payout
ratio
0.859
0.830
0.873
0.823
2.476
6.693
0.514
0.579
Insider holding
ratio
Investment ratio
Fixed assets to total
assets ratio
0.756
0.635
2.039
5.510
0.635
0.607
0.755
0.772
Times interest
earned
Cash flow to long
term debt
0.836
0.778
0.827
0.732
Turnover rate of
working capital
Turnover rate of
inventory
0.788
0.777
0.714
0.736
Turnover rate of
account receivable
Gross margin
growth ratio
Sales revenue
growth ratio
0.782
0.693
0.665
0.526
0.548
0.641
Cash flow to short
0.871
term and long term
debt ratio
Total explained variance
0.813
4
4.3. Factor analysis
This paper collected the samples of 34 pairs of financial distress
and non-bankruptcy firms listed in the TSEC, between 1999 and
2006. The main variables are 37 ratios for the predictive financial
distress model factors. This research used the SPSS statistical software to conduct factor analysis and principle component analysis
(PCA) with varimax for rotation (VARIMAX), in order to make the
factor structure easier and simpler to explain. The principle for
the selection of factors is based on Kaiser’s criteria, meaning that
the eigenvalue greater than 1 is a common factor, the absolute value of the factor loadings is greater than 0.5 and the communality
is greater than 0.8 in order to obtain suitable factors.
In total, we compiled 33 financial ratios and 4 non-financial ratios. In an attempt to reduce dimensionality, we ran a factor analysis to test whether the differences between these 37 variables
were significant for each variable. If the difference was not significant (low factor loadings or communality values), the variable was
considered to be non-informative. Table 1 shows the factor loadings, communality, the eigenvalues and the explained variance
for each variable. As a result, 18 variables presented high factor
loadings or communality values. These variables were chosen to
be used in the input vector, while the remaining 19 variables were
discarded. In addition, the total explained variance was 75.776%.
We used the factor analysis to process the experiment a second
time. Table 2 shows that 5 variables were discarded, and that the
total explained variance was 85.288%. Due to the better performance in the total explained variance value, we can assume that
the factor analysis is not yet the optimal solution. Therefore, we
used the factor analysis to process the experiment a third time.
Table 3 shows that two variables were discarded, and that the total
explained variance was 91.876%. Therefore we used the factor
analysis to process the experiment a fourth time. However, Table
4 shows there were no suitable variables to be discarded, and the
total explained variance was down to 88.228%. Therefore, we can
were sure that the optimal factor analysis was the one we carried
out the third time, where the performance was the highest at
91.876%.
5
6
7
8
9
10
11
75.776
2.012
4.571
1.646
4.450
1.110
2.999
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W.-S. Chen, Y.-K. Du / Expert Systems with Applications 36 (2009) 4075–4086
Table 2
2nd Factor analysis results
Table 4
4th Factor analysis results
Factors
Variables
Factor
loadings
Communality
Eigenvalues
Explained
variance
Factors
Variables
Factor
loadings
Communality
Eigenvalues
Explained
variance
1
Return on asset
(ROA)
Return on equity
(ROE)
Earnings per
share (EPS)
Margin before
interest and tax
(BEFM)
0.913
0.904
3.497
19.427
1
0.962
0.961
0.988
0.986
2.969
26.989
0.903
0.923
Gearing ratio
Debt to equity
ratio
Debt/equity (DE)
0.942
0.973
0.897
0.897
2
0.923
0.929
2.779
25.259
0.759
0.717
0.918
0.923
0.910
0.931
Gearing ratio
Debt to equity
ratio
Debt/equity (DE)
Debt ratio
0.962
0.961
0.978
0.976
Return on asset
(ROA)
Earnings per
share (EPS)
Return on equity
(ROE)
0.915
2.047
18.613
0.968
0.789
0.920
0.393
0.916
0.194
3
Current ratio
Acid-test ratio
0.896
0.892
0.939
0.940
Cash flow to
total debt ratio
Cash flow ratio
Inventory to
total assets ratio
0.937
0.939
0.656
0.909
0.868
0.936
0.921
0.975
0.975
17.366
Inventory to total
assets ratio
Inventory to sales
ratio
Current ratio
Acid-test ratio
1.910
4
0.891
0.854
Turnover rate of
fixed assets
Turnover rate of
total assets
Current assets to
total assets
0.840
0.775
0.811
0.761
0.649
0.869
Cash flow to total
debt ratio
Cash flow ratio
Cash flow to short
term and long
term debt ratio
0.830
0.835
0.811
0.642
0.869
0.489
2
5
6
Total explained variance
3.492
19.401
3
2.296
12.755
4
11.659
Total explained variance
2.076
11.536
1.892
10.509
85.288
Factors
Variables
Factor
loadings
Communality
Eigenvalues
Explained
variance
1
Debt to equity
ratio
Gearing ratio
Debt/equity (DE)
0.970
0.993
3.011
23.164
0.969
0.943
0.994
0.973
Return on asset
(ROA)
Earnings per
share (EPS)
Return on equity
(ROE)
0.923
0.935
2.759
21.227
0.917
0.930
0.909
0.930
3
Current ratio
Acid-test ratio
Current assets to
total assets
0.894
0.877
0.602
0.929
0.945
0.763
2.106
16.203
4
Cash flow to
total debt ratio
Cash flow ratio
0.950
0.934
2.038
15.673
0.940
0.943
Inventory to
total assets ratio
Inventory to
sales ratio
0.927
0.889
0.874
0.788
5
equity ratio, gearing ratio, debt/equity (DE), return on asset
(ROA), earnings per share (EPS), return on equity (ROE), current ratio, acid-test ratio, current assets to total assets, cash flow to total
debt ratio, cash flow ratio, inventory to total assets ratio, and
inventory to sales ratio.
5. The FDP modeling phase
5.1. ANN experiments and results
Table 3
3rd Factor analysis results
2
88.228
This process uses the finance and non-finance ratios, and constructs a financial distress prediction model after carrying out a
second time factor analysis. The variables are then loaded as
ANN input nodes. In addition, we also apply these experiment
parameters to investigate the past 2 seasons, the past 4 seasons,
the past 6 seasons, and the past 8 seasons before the financial distress occurred, for the sake of prediction accuracy. In this experiment, we will use the BPN as the ANN algorithm. In addition, the
training sample and the testing sample will adopt the 80:20 ratio.
In terms of bankruptcy prediction, whether or not the prediction is accurate is routinely measured by three quantities: Type I
Error Rate, Type II Error Rate, and Total Error Rate. ‘‘Type I Error Rate”
means that the error rate for the risk can not categorize the normal
company as a normal company, ‘‘Type II Error Rate” means that the
error rate for the risk can not categorize the bankruptcy company,
and ‘‘Total Error Rate” means the combined ‘‘Type I Error Rate” and
‘‘Type II Error Rate”. Table 5 shows the relationship among these
three error rate types. The formula for each error rate is listed as
follows:
Y2
Y3
Y4
Type II Error Rate ¼
Y6
ðY 2 þ Y 4 Þ
Total Error Rate ¼
Y9
Type I Error Rate ¼
Total explained variance
2.029
15.609
91.876
ð4Þ
ð5Þ
ð6Þ
Table 5
The relationship with type I, II, and total error rates
Prediction
After the three times factor analysis, 13 variables presented
higher factor loadings or communality values. These variables
were chosen to be used in the input vector, while the remaining
24 variables were discarded. The selected variables were debt to
Actually
Normal
Bankruptcy
Sum
Sum
Normal
Bankruptcy
Y1
Y4
Y7
Y2
Y5
Y8
Y3
Y6
Y9
W.-S. Chen, Y.-K. Du / Expert Systems with Applications 36 (2009) 4075–4086
5.1.1. The experiment using a non-factor analysis
This experiment obtains a result after using 37 original ratio
variables that have not yet obtained a result by factor analysis.
As shown in Table 6, the testing data has an estimate accuracy rate
as high as 82.14%, with an error rate of 17.86% for the past 2 seasons. However, the accuracy rate reduces to 60%, and the error rate
rises to 40% when measured over the past 8 seasons. The closer the
financial crisis the higher the accuracy will be.
5.1.2. The experiment with the 1st factor analysis
This experiment obtains a result after using 18 original ratio
variables of this research that have undergone 1st factor analysis.
As shown in Table 7, the testing data has an estimate accuracy rate
as high as 78.57%, with an error rate of 21.43% for the past 2 seasons. However, the accuracy rate reduces to 66.36%, and the error
rate rises to 33.64% when measured over the past 8 seasons. Similar to the above experiment, the closer the financial crisis the
higher the accuracy will be.
5.1.3. The experiment with 2nd factor analysis
This experiment obtains a result after using 13 original ratio
variables of this research that have undergone 2nd factor analysis.
As shown in Table 8, the testing data has an estimate accuracy rate
as high as 75%, with an error rate of 25% for the past 2 seasons.
Table 6
The accuracy for the ANN model with non-factor analysis
Training data
Normal
2
4
6
8
Accuracy
Average
Accuracy
Average
Accuracy
Average
Accuracy
Average
rate
rate
rate
rate
Testing data
Bankruptcy
87.03%
94.44%
90.74%
89.91%
92.67%
91.28%
91.41%
95.71%
93.56%
95.85%
93.55%
94.70%
Normal
Bankruptcy
92.86%
71.43%
82.14%
100.00%
55.56%
77.78%
87.80%
65.85%
76.83%
74.55%
45.45%
60.00%
Table 7
The accuracy for the ANN model with 1st factor analysis
Training data
Normal
2
4
6
8
Accuracy
Average
Accuracy
Average
Accuracy
Average
Accuracy
Average
rate
rate
rate
rate
Testing data
Bankruptcy
90.74%
84.48%
86.11%
87.16%
85.32%
86.24%
83.44%
86.50%
84.97%
93.09%
88.48%
90.78%
Normal
85.71%
88.89%
65.85%
67.27%
Bankruptcy
71.43%
78.57%
48.15%
68.52%
68.29%
67.07%
65.45%
66.36%
Table 8
The accuracy for the ANN model with 2nd factor analysis
Training data
Normal
2
4
6
8
Accuracy
Average
Accuracy
Average
Accuracy
Average
Accuracy
Average
rate
rate
rate
rate
87.04%
Testing data
Bankruptcy
77.78%
82.41%
86.24%
86.24%
86.24%
87.73%
83.44%
85.58%
86.18%
81.57%
83.87%
Normal
78.57%
92.59%
80.49%
78.18%
Bankruptcy
71.43%
75.00%
51.85%
72.22%
48.78%
64.63%
52.73%
65.45%
4081
However, the accuracy rate reduces to 65.45%, and the error rate
rises to 34.55% when measured over the past 8 seasons. Similar
to the above experiment, the closer the financial crisis the higher
the accuracy will be.
5.2. DM experiments and results
Clustering analysis finds groups, each very different from the
other. However, within a group all members are very similar. Unlike classification, the class label of each group is not known. Clustering is a way to naturally segment data into groups, whereas
classification is a way to segment data by assigning it into groups.
Briefly, a good clustering method will produce high quality clusters
with high intra-class similarity and low inter-class similarity (Chen
& Chen, 2006). However, how good a cluster is ultimately depends
on the opinion of the user. In our experiment, we used the partitioning methods to cluster the datasets for the financial distress
prediction model. The partitioning methods construct a partition
of a database of N objects into a set of k clusters. Usually, they start
with an initial partition and then use an iterative control strategy
to optimize an objective function.
The K-means algorithm (Han & Kamber, 2001) is a wellknown and commonly used clustering algorithm. It takes input
parameter k and partitions data into k clusters. First, we select
k objects to represent the cluster centers. The remaining objects
are then assigned to the cluster whose center is closest to the
object. Then, it computes the mean value for each cluster as
new cluster centers. This process is iterated until the criterion
function converges.
The same as with the ANN experiment, this process also uses a
finance and non-finance ratio, and constructs the financial distress
prediction model after a second time factor analysis. We apply the
K-means algorithm to investigate the past 2 seasons, the past 4
seasons, the past 6 seasons, and the past 8 seasons before the
occurrence of financial distress to ensure prediction accuracy. After
the K-means algorithm implementation, we decided to adopt
10–15 clusters to analyze the prediction accuracy.
5.2.1. The experiment with non-factor analysis
This experiment obtains a result after using 37 original ratio
variables of this research that haven’t yet undergone a factor analysis. As shown in Table 9, the data has an estimate accuracy rate as
high as 78.57%, with an error rate of 21.43% for the past 2 seasons.
However, the accurate rate reduces to 56.36%, and the error rate
rises to 43.64%, when measured over the past 8 seasons. The closer
the financial crisis the higher the accuracy will be.
5.2.2. The experiment with 1st factor analysis
This experiment obtains a result after using 18 original ratio
variables of this research that have undergone a 1st factor analysis.
As shown in Table 10, the data has an estimate accuracy rate as
high as 75%, with an error rate of 25% for the past 2 seasons. However, the accurate rate reduces to 56.36%, and the error rate rises to
43.64% when measured over the past 8 seasons. Similar to the
above experiment, the closer the financial crisis the higher the
accuracy will be.
5.2.3. The experiment with 2nd factor analysis
This experiment obtains a result after using 13 original ratio
variables of this research that have undergone 2nd factor analysis.
As shown in Table 11, the testing data has an estimate accuracy
rate as high as 75%, with an error rate of 25% for the past 2 seasons.
However, the accurate rate reduces to 56.36%, and the error rate
rises to 43.64% when measured over the past 8 seasons. Similar
to the above experiment, the closer the financial crisis the higher
the accuracy will be.
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W.-S. Chen, Y.-K. Du / Expert Systems with Applications 36 (2009) 4075–4086
Table 9
The accuracy for the clustering model with non-factor analysis
10 Clusters
Accuracy
Normal
2
4
6
8
Accuracy
Average
Accuracy
Average
Accuracy
Average
Accuracy
Average
Bankruptcy
100%
57.14%
78.57%
74.07%
77.78%
75.93%
51.22%
85.37%
68.29%
47.27%
87.27%
67.27%
11 Clusters
Accuracy
Normal
Bankruptcy
50.00%
85.71%
67.86%
88.89%
55.56%
72.22%
100%
48.78%
64.63%
85.45%
36.36%
60.91%
12 Clusters
Accuracy
Normal
13 Clusters
Accuracy
Bankruptcy
50.00%
85.71%
67.86%
88.89%
55.56%
72.22%
100%
51.22%
75.61%
41.82%
78.18%
60.00%
Normal
14 Clusters
Accuracy
Bankruptcy
100%
57.14%
78.57%
62.96%
70.37%
66.67%
100%
51.22%
75.61%
40.00%
78.18%
59.09%
Normal
15 Clusters
Accuracy
Bankruptcy
Normal
100%
57.14%
78.57%
88.89%
55.56%
72.22%
97.56%
51.22%
74.39%
50.91%
76.36%
63.64%
85.71%
14 Clusters
Accuracy
15 Clusters
Accuracy
Bankruptcy
57.14%
71.43%
88.89%
55.56%
72.22%
60.98%
73.17%
67.07%
96.36%
16.36%
56.36%
Table 10
The accuracy for the clustering model with 1st factor analysis
2
4
6
8
Accuracy
Average
Accuracy
Average
Accuracy
Average
Accuracy
Average
10 Clusters
Accuracy
11 Clusters
Accuracy
Normal
Normal
Bankruptcy
100%
35.71%
67.86%
70.37%
51.85%
61.11%
92.68%
29.27%
60.98%
72.73%
40.00%
56.36%
12 Clusters
Accuracy
Bankruptcy
100.00%
50.00%
75.00%
100.00%
40.74%
70.37%
100%
19.51%
59.76%
100.00%
14.55%
57.27%
Normal
13 Clusters
Accuracy
Bankruptcy
Normal
Bankruptcy
Normal
Bankruptcy
Normal
Bankruptcy
100.00%
50.00%
75.00%
100.00%
37.04%
68.52%
100%
19.51%
59.76%
100.00%
21.82%
60.91%
100%
50.00%
75.00%
100.00%
40.74%
70.37%
53.66%
51.22%
52.44%
100.00%
23.64%
61.82%
100%
50.00%
75.00%
100.00%
40.74%
70.37%
100.00%
34.15%
67.07%
100.00%
21.82%
60.91%
100.00%
50.00%
75.00%
100.00%
37.04%
68.52%
100.00%
34.15%
67.07%
100.00%
21.82%
60.91%
12 Clusters
Accuracy
13 Clusters
Accuracy
14 Clusters
Accuracy
15 Clusters
Accuracy
Table 11
The accuracy for the clustering model with 2nd factor analysis
10 Clusters
Accuracy
Normal
2
4
6
8
Accuracy
Average
Accuracy
Average
Accuracy
Average
Accuracy
Average
11 Clusters
Accuracy
Bankruptcy
100.00%
21.43%
60.71%
100.00%
37.04%
68.52%
82.93%
65.85%
74.39%
58.18%
56.36%
57.27%
Normal
Bankruptcy
100.00%
35.71%
67.86%
100.00%
37.04%
68.52%
82.93%
65.85%
74.39%
83.64%
29.09%
56.36%
Normal
Bankruptcy
100.00%
50.00%
75.00%
100.00%
37.04%
68.52%
82.93%
65.85%
74.39%
65.45%
60.00%
62.73%
6. The FDP comparing phase
After the implementation for the FDP modeling phase, we will
compare the BPN and clustering approaches with the accuracy
rate, Type II error rate, and factor analysis. The detail descriptions
will be discussed as following sections.
6.1. The accuracy rate for BPN and clustering
As is evident by the above-mentioned results in Fig. 4, the BPN
model presents the prediction performance by non-factor analysis,
after the first-time factor analysis, and after the second time factor
analysis. The result shows that the accuracy rate has the worst
trend from the past 2 seasons to the past 8 seasons prior to the
occurrence of the financial crisis. In addition, the BPN model shows
that the closer the crisis the higher the accuracy rate becomes.
As seen by the above-mentioned results shown in Fig. 5, the
clustering model shows the prediction performance by non-factor
analysis, after first-time factor analysis, and after the second time
factor analysis. As a result, the accuracy rate is also shown the
Normal
71.43%
Bankruptcy
50.00%
60.71%
100.00%
25.93%
62.96%
82.93%
65.85%
74.39%
65.45%
60.00%
62.73%
Normal
Bankruptcy
71.43%
50.00%
60.71%
100.00%
51.85%
75.93%
68.29%
68.29%
68.29%
61.82%
61.82%
61.82%
Normal
Bankruptcy
92.86%
57.14%
75.00%
70.37%
74.07%
72.22%
68.29%
68.29%
68.29%
74.55%
56.36%
65.45%
worse and worse trend as BPN model. In addition, the clustering
model becomes more accurate the closer the crisis.
6.2. The type II error rate for BPN and clustering
As seen by the above-mentioned results shown in Fig. 6, the
BPN model presents the Type II error rate by non-factor analysis,
after first-time factor analysis, and after the second time factor
analysis. It shows that the Type II error rate increases for each factor analysis, while the accuracy rate decreases from the past 2 seasons to the past 8 seasons prior to the financial crisis. In addition,
the BPN model becomes more accurate the closer the crisis and the
Type II error rate becomes lower.
As seen by the above-mentioned results shown in Fig. 7, the
clustering model presents the Type II error rate by non-factor
analysis, after first-time factor analysis, and after the second time
factor analysis. It indicates that the Type II error rate has approximately the same increasing trend as the BPN model, while the
accuracy rate decreases similar to the BPN model. The only exception is the Type II error rate which is better in the 2nd factor anal-
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The Accuracy Rate for the BPN
90.00%
80.00%
past 2 seasons
70.00%
60.00%
past 4 seasons
50.00%
40.00%
past 6 seasons
30.00%
20.00%
past 8 seasons
10.00%
0.00%
None
1st
2nd
past 2 seasons
82.14%
78.57%
75.00%
past 4 seasons
77.78%
68.52%
72.22%
past 6 seasons
76.83%
67.07%
64.63%
past 8 seasons
60.00%
66.36%
65.45%
Fig. 4. The accuracy rate for the BPN.
The Accuracy Rate for Clustering
80.00%
past 2 seasons
60.00%
past 4 seasons
40.00%
past 6 seasons
20.00%
past 8 seasons
0.00%
None
1st
2nd
past 2 seasons
73.81%
74.31%
66.67%
past 4 seasons
71.91%
68.21%
69.36%
past 6 seasons
72.56%
61.18%
72.36%
past 8 seasons
61.21%
59.70%
61.06%
Fig. 5. The accuracy rate for clustering.
ysis than in the non-factor analysis over the past 6 seasons. Nevertheless, in summary we get that the closer the crisis point, the lower the Type II error rate in the clustering model.
6.3. The factor analysis for BPN and clustering
In this comparison, we average the accuracy rate of BPN and the
clustering model for each factor analysis and over 2, 4, 6, and 8 seasons. In Fig. 8, we can see that the accuracy rate (non-factor analysis) with the BPN model is better than with the clustering model,
with the exception of the past 8 seasons. In Fig. 9, we can see that
the accuracy rates (1st factor analysis) with the BPN model are all
better than with the clustering model. In Fig. 10, we can see that
the accuracy rate (2nd factor analysis) with the BPN model is better than with the clustering model, with the exception over the
past 6 seasons.
7. Conclusions
This research aimed at the financial and the non-financial ratios
in the financial statement, and used the BPN and the clustering
model to compare the performance of the financial distress
predictions, in order to find a better early-warning method. This
research took 34 companies that were facing a financial crisis,
and matched them with 34 normal companies of the similar industry. In addition, we adopted the necessary dataset from the TSEC
database and sampled them into the past 2, 4, 6, 8 seasons prior
to the financial crisis occurrence. This data was then used to carry
out a statistical factor analysis, with each ratio variable being generated going into BPN and clustering methods in order to make a
comparison.
After the experiments, we summarized four critical contributions. First, the more time we used factor analysis, the less accurate
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The Type 2 Error Rate for the BPN
60.00%
past 2 seasons
50.00%
40.00%
past 4 seasons
30.00%
past 6 seasons
20.00%
10.00%
0.00%
past 8 seasons
None
1st
2nd
past 2 seasons
28.57%
28.57%
28.57%
past 4 seasons
44.44%
51.85%
48.15%
past 6 seasons
34.15%
31.71%
51.22%
past 8 seasons
54.55%
34.55%
47.27%
Fig. 6. The type 2 error rate for the BPN.
The Type 2 Error Rate for Clustering
90.00%
80.00%
past 2 seasons
70.00%
60.00%
past 4 seasons
50.00%
40.00%
past 6 seasons
30.00%
20.00%
past 8 seasons
10.00%
0.00%
None
1st
2nd
past 2 seasons
33.34%
52.38%
55.95%
past 4 seasons
38.27%
58.64%
56.17%
past 6 seasons
39.84%
74.71%
33.34%
past 8 seasons
37.88%
76.36%
46.06%
Fig. 7. The type 2 error rate for clustering.
the results for the BPN and clustering approaches. In our experiments, we found that when we applied all of the 37 variables with
non-factor analysis into the BPN and clustering models, we could
obtain a better prediction performance except for the past 8 seasons in the BPN model and for the past 2 seasons in the clustering
model.
Second, the closer we get to the time of the actual financial distress, the more accurate the prediction will be. For example, the
accuracy rate with the non-factor analysis for 2 seasons before
the financial distress occurs is 82.14% in BPN, while it is only 60%
over 8 seasons. The results are similar for the clustering model,
where the accuracy rate with non-factor analysis for 2 and 8 seasons before the occurrence of financial distress are 73.81% and
61.21%, respectively.
Third, most investors are concerned with the Type II error rate
and avoid investing in these companies. Our empirical results
show that factor analysis increases the error forecasts of classifying
companies with a potential financial crisis as a normal company.
Moreover, we also found that the average rate of the Type II error
in the clustering model is higher than in the BPN model. Therefore,
the prediction performance for the clustering approach is more
aggressively influenced than the BPN model.
Finally, the BPN approach obtains a better prediction accuracy
than the DM clustering approach in developing a financial distress
prediction model, with the exception that the accuracy rate (nonfactor analysis) for the past 8 seasons model and the accuracy rate
(2nd factor analysis) for the past 6 seasons is lower with the BPN
model.
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BPN vs. Clustering Model
Accuracy Rate
90.00%
80.00%
70.00%
60.00%
50.00%
BPN
40.00%
Clustering
30.00%
20.00%
10.00%
0.00%
2 Seasons
4 Seasons
6 Seasons
8 Seasons
Before the Occurrence of Financial Distress
Fig. 8. The accuracy rate with non-factor analysis for the BPN and clustering comparison.
BPN vs. Clustering Model
Accuracy rate
90.00%
80.00%
70.00%
60.00%
50.00%
BPN
40.00%
Clustering
30.00%
20.00%
10.00%
0.00%
2 Seasons
4 Seasons
6 Seasons
8 Seasons
Before the Occurrence of Financial Distress
Fig. 9. The accuracy rate with 1st analysis for the BPN and clustering comparison.
BPN vs. Clustering Model
Accuracy rate
80.00%
70.00%
60.00%
50.00%
BPN
40.00%
Clustering
30.00%
20.00%
10.00%
0.00%
2 Seasons
4 Seasons
6 Seasons
8 Seasons
Before the Occurrence of Financial Distress
Fig. 10. The accuracy rate with 2nd analysis for the BPN and clustering comparison.
In future research, additional artificial intelligence techniques,
such as other neural network models, classification mining, genetic
algorithms, and others, could also be applied. And certainly,
researchers could expand the system so as to deal with more financial datasets.
Acknowledgements
We also gratefully acknowledge the Editor and anonymous
reviewers for their valuable comments and constructive
suggestions.
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