This paper proposes a synoptic methodology to evaluate the determinants of audit fees by utilising Neural Networks. First, a brief discussion is presented to highlight the significant application of Neural Network in the areas of financial management; second the framework of proposed methodology has been outlined to examine the implication of audit fees on target sample. The underlying rational of this paper is to establish NNs as a diagnostic tool to assess the effect of audit fees on firms, which indeed warrants further empirical investigation. The importance of NNs emerges from the fact that if external and internal audit fees can be disseminated by employing this methodology which is perceived more significantly robust than other econometric models, then accounting standards can be improved.Neural Networks and Audit Fee

Rama Prasad Kanungo

English

Research Papers in Economics

 
Neural Networks: Is it hermeneutic? 
 
 
 
 
Rama Prasad Kanungo
1 
 
 
 
 
                                                
1 Rama Kanungo is the Research Co-ordinator of the Asian Accounting, Finance and Business 
Research Unit, Cardiff Business School, Colum Drive, Cardiff, CF10 3EU, 
UK.Email:Kanungomba@hotmail.com 
 
 
  
 
Abstract 
 
 
This paper proposes a synoptic methodology to evaluate the determinants of audit fees 
by utilising Neural Networks. First, a brief discussion is presented to highlight the 
significant  application  of  Neural  Network  in  the  areas  of  financial  management; 
second the framework of proposed methodology has been outlined to examine the 
implication of audit fees on target sample. The underlying rational of this paper is to 
establish NNs as a diagnostic tool to assess the effect of audit fees on firms, which 
indeed warrants further  empirical  investigation.  The  importance of NNs emerges 
from the fact that if external and internal audit fees can be disseminated by employing 
this methodology which is perceived more significantly robust than other econometric 
models,  then  accounting  standards  can  be  improved.Overview of Neural Networks: Efficacy in Finance  
 
The applied process of Neural Networks and the cognitive competence of our 
brain are functionally coterminous. Both the processes learn through different patterns 
and predict most probable outcomes. However, the function of NNs is very much 
limited with reference to our real synaptic versatility. The origin of neural networks 
dates back to the 1940s.  McCulloch and Pitts (1943) and Hebb (1949) researched 
networks of  simple computing  devices that could model neurological activity and 
learning within these networks, respectively.  Later, the work of Rosenblatt (1962) 
focused  on  computational  ability  in  perceptrons,  or  single-layer  feed-forward 
networks.    Proofs  showing  that  perceptrons,  trained  with  the  Perceptron  Rule  on 
linearly  separable  pattern  class  data,  could  correctly  separate  the  classes  truly 
generated excitement among researchers and practitioners. 
NNs are a form of multiprocessor computing system with simple processing 
elements,  high  degree  of  interconnectedness,  simple  scalar  message  and  adaptive 
interaction  between  each  element  (Smith,  1996).  Each  simple  element  is  like  our 
cerebral neurons competent of propagating systematic reception to next one following 
a layered matrix. This matrix is highly connected and conduits message in a scalar 
form. They adapt the message and process it to identify an optimal outcome. The 
main subjectivity of such process minimises the error through a sequential elimination 
approach. Haykin(1994) states that NNs resemble brain in two ways, first, knowledge 
is  acquired  by  the  network  through  a  learning  process  and  second,  interneuron 
connection strengths known as synaptic weights are used to store the knowledge . 
Smith (1996) presented single unit adaptive network in this following diagram 
 
  
 
                             Y=I0 or I1 
                             Linear threshold Unit      
 
 W0      W1         Wb   
 
 
 
I0                      I1               Bias Unit=1 
 
 This network has two inputs and one output. All are binary by structural mode. The 
output is outlined as 
1 if W0* I0 + W1* I1+ Wb>0 
0 if W0* I0 + W1* I1+ Wb<=0 
 
For the purpose of simple presentation we say output is 1 if either I0 or I1 is 1 
 
The NNs identify the change by an amount proportional to the difference between the 
desired output and the actual output.  This is  referred as Perceptron  learning rule, 
which is presented below in the Eq. (1). 
Recently NNs are in vogue as a diagnostic tool to examine the topology of 
financial applications. Fadlalla and Lin (2004) state that some major characteristics of 
such applications are to investigate data intensity, unstructured and noisy data, high 
uncertainty  scenarios  and  hidden  relationship  between  parameters.  So  far  many 
studies  have  utilised  NNs  to  examine  the  predictive  aspects  of  such  applications. 
Essentially,  during  1993-1995  NNs  were  increasingly  been  used  in  the  financial 
studies.  However,  so  far  NNs  have  mainly  been  unutilised  for  forecasting  and 
asymmetric prediction, so this paper intends to propose NNs in a different context to 
measure the binary effects of certain parameters such as audit fees. 
 
The following table illustrates some key studies where NNs are employed to explore studies in 
financial applications:  
Study  Domain  Year 
Altman, Marco, and Varetto  1994 
Coleman, Graettinger and Lawrence  1991 
Klemic  1993 
Odom and Sharda  1990 
Raghupati, Schkade and Raju  1991 
Rahimiana et al  1993 
Salchenberger, Cinar and Lash  1992 
Tam  1991 
Tam and Kiang  1992 
Wilson and Sharda 
Bankruptcy prediction 
1994 
Ahmadi  1990 
Baba et al  1993 
Barker  1990 
Barr and Mani  1994 
Bergerson and Wunsch  1991 
Berry and Trigueiros  1993 
Bosarge  1991 
Cheng, Wagner and Lin  1996 
Chenoweth and Obradovic  1995 
Chiang, Urban and Blabridge  1996 
Chuah  1992 
Collard  1993 
Ganesh  1994 
Kamijo and Tanigawa 
Stock-market forecasting 
1990 Kimoto and Asakawa  1990 
Kryzanowski, Gellar and Wright  1993 
March  1995 
Quah, Tan and Heng  1993 
Refenes  1993 
White  1988 
Yoon and Swales 
 
1991 
Morase  1990 
Reilly et al  1991 
Roy and Cosset  1994 
Van Eyen and Cronjie 
Credit analysis 
1994 
Vishwakrama  Business-cycle recognition  1994 
Dutta and Shekhar  Bond rating  1988 
Source: Fadlalla, A. and Lin, C. (2004)   
 
Outline of Proposed methodology: Audit Fees 
 
Following  Kutsurelis’s  (1998)  study  to  examine  the  financial  market  this 
methodology  proposes  a  similar  approach.  In  the  light  of  previous  researches 
undertaken it can be envisaged that in the place of assessing the accuracy of financial 
forecasting, it can be potentially employed to investigate the effect of audit fee on 
public or private sector firms.  In this discussion it has been proposed to use the 
network utilising two adaptive functions, one is a Logistic function f(x)=1/(1+exp(-
X))  and  other  one  is  the  Gaussian  function f(x)=exp(-X
2).  Both  the  functions  are 
utilised in the study undertaken by Kutsurelis. Also these methods were used by both 
Kartalopoulos  (1996)  and  Haykin  (1994)  to  examine  the  financial  forecasting 
accuracy. After calculating the functions, each one will be employed as input nodes in 
the final NNs model. The prior assumption in this instance is drawn upon the concept 
that  NNs  is  highly  effective  to  identify  signals  and  eliminate  noisy  data  flow. 
Particularly over a long period and lagged time series data where unstructured nature 
and hidden relationship in variables are not correctly identified. Hence it is presumed 
that such approach would be more appropriate where a sampling 5-10 years data is 
compiled and collapsed on target firms.  Furthermore, least square approximation and 
random  sampling  do  not  always  provide  a  robust  calculation.  Therefore,  a  log 
linearisation  approach  is  more  practical  in  this  instance  to  establish  the  maxima 
threshold of parameters. 
It would be reasonable to focus these types of research on the backpropagation 
algorithm learning method. This method has often been employed in many previous 
researches. Backpropagation algorithm focuses to minimise residual error between 
NNs  output  and  actual  desired  output  value  (Kutsurelis,  1998).  A  brief  view  of 
backpropagation  model  is  presented  below  following  Dhar  and  Stein  (1996)  and Kutsurelis (1998). The BPN model has been selected for this proposed methodology 
for  two  reasons,  first,  it  converges  on  the  error  minimisation  problem;  second,  it 
provides optimal solution to high frequency momentum and learning rates. Following 
NNs it is rational to theorise that output node corresponds to 1= positive value, 0= 
negative value in terms of the effect of audit fees on the sample firms. The input 
nodes represent financial ratios that the model will use to predict the effect of audit 
fees as a whole on the sample pool. The audit fee would be categories into external 
and  internal  fees  to  conclude  each  ones  effect  on  firms.  This  would  differentiate 
apparent effects of the each category on the firms. In this approach the ratios used by 
Altman et. al. (1994) with some variations are feasible and often been investigated, 
thus seem more adaptable in this context. The ratios proposed are:  
Working Capital/Total Assets 
Total Liabilities/Total Assets 
External Audit Fees/ Total Assets 
Internal Audit Fees/Total Assets 
ROI/Total Assets 
Cash Flow/ Total Debt 
Cash/ Current Liabilities 
Current Assets/Current Liabilities 
EBIT/Total Interest Payments 
Working Capital/Total Assets 
Initially, it is expected that these ratios should be calculated by utilising above two 
functions and subsequently each output would serve as inputs in the final model. The 
basic  concepts  of  BPN,  which  is  sometimes  referred as  multi-layered perceptrons 
(MLPs)  and  radial  Basic  Function  Networks  (RBF)  is  described  in  the  following 
section. 
Usually BP uses a gradient descent algorithm which follows the error curvature by 
moving down the slope.  In this study it is imperative to minimise the total squared 
errors by repeated error elimination process, such as using BNP. The following BP 
error minimisation models are adapted from Kaastra and Boyd (1996) 
 
            M        M  N  
E= ½ ￿ En =  ￿  ￿ (tni – oni)…………………………………………(1) 
           n          n   i  
Where E is the total error of all neural patterns, En represents the error pattern n, the 
index n ranges over the set of input patterns, and I refers to the ith output of neuron. 
The variable tni is the desired output for the ith output neuron when the nth pattern is 
presented,  and  oni  is  the  actual  output  of  the  ith  output  neuron  when pattern  n  is 
presented. The adaptive interface as learning rule to adjust the weight between neuron 
I and j is defined as: 
 
￿ni= (tni-oni) oni (1-oni)…………………………………………………(2) 
                         N 
￿ni= oni (1- oni) ￿ ￿nk wjk ….……………………………………………(3) 
                         k 
￿wij (h+1)= ￿ (￿ni oni)………………………………………………….(4) 
 
Where h is the presentation number, ￿ni is   the error signal neuron I for pattern n, and 
￿  is  the  learning  rate.  The  learning  rate  is  a  constant  of  proportionality  which 
determines the size of the weight changes. Essentially the weight changes of neurons 
are proportional to the impact of the weight from the neurons on the error. The error 
signal for an output neuron and a hidden neuron are calculated by Eq. (3) and (4) by 
using simplified partial differential equations. Kaastra and Boyd (1996) suggests that 
to  increase  the  learning  rate,  thus  to  enhance  the  backpropagation  training  time 
without leading to oscillation, a momentum term needs to be included in BP learning 
rule. They further add that this momentum term determines how past weight changes 
affect current weight changes. The modified training rule as defined by them is  
 
￿wij (h+1)= ￿ (￿ni oni)+ ￿ ￿wij (h)…………………………………….(5) 
 
However NNs software programme usually provides default values for learning rate 
and momentum that mostly adjust the high frequency oscillation. 
Mainly running the NNs consists of in two fold approaches. First, forwardpass 
when the outputs are calculated and the error at the output units are calculated; second 
backpropagating or backwardpass, the output error is used to alter the weights on the 
output units and the error at the hidden nodes is calculated, subsequently the weights 
on the hidden nodes are altered using these values. Thus the model optimises error to 
a  minimal  threshold.  Dhar  and  Stein  (1996)  state  that  by  recursive  backward propagation such errors are minimised and all the weights are adjusted to converge on 
error minimisation solution. 
Essentially, it is secure to save the data in SPSS and subsequently import the 
files into NNs software package, Neuroshell 2 as patterned files. The ratios would be 
converted using SPSS commands to calculate logistic function and Gaussian function 
values, respectively, i.e., f(x) =1/(1+exp(-X)) and f(x)=exp(-X
2). Furthermore, a Ward 
Network would be used to train the Network. Ward Network is a BPN with one input 
layer, three hidden layers and one output layer. Each layer is known as a slab. Each 
slab is customarily consists of one to sixteen individual neurons depending upon the 
location within the networks.  Each slab has a different activation function. In this 
research aforesaid two functions are recommended only to restrict the complicated 
computational procedure. 
However the application of Neural Networks in this context is subjective to 
further  rigour  of  empirical  estimation.  The  essence  of  robustness  can  only  be 
established  upon  critical  examination  of  such  rigour,  which  requires  diligence  in 
pooling the data and layering it with necessary commands.  
 Bibliography 
 
 
Altman,E.  I.,  Marco,  G.  and  Veretto,  F.  (1994)  ‘Corporate  Distress  Diagnosis: 
Comparisons using Linear Discriminant Analysis and Neural Networks’, Journal of 
Banking and Finance, Vol.18, No.3, pp 505-529. 
 
 
Dhar, V. and Stein, R. (1996) ‘Intelligent Decision Support Methods: The Science of 
Knowledge Work (Ed.), Prentice Hall Business Publishing, NJ, USA. 
 
 
Fadlalla, A. and Lin, C. (2004) ‘An Analysis of the Application of Neural Networks 
in  Finance’,  Working  paper,  Department  of  Computer  and  Information  Services, 
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Haykin,  S.  (1994)  ‘Neural  Networks:  A  Comprehensive  Foundation’,  MacMillan 
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Hebb, D. O. (1949) ‘The Organization of Behavior’ New York: John Wiley. 
 
 
Kaastra,  I.  and  Boyd,  M.(1996)  ‘Designing  a  Neural  Network  for  Forecasting 
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Kartalopoulos, S. V. (1996) ‘Understanding Neural Networks and Fuzzy Logic: Basic 
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Neural Networks: Is it hermeneutic?

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Neural Networks: Is it hermeneutic?

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