Based on the Efficiency Coefficient-BP Neural Network Study of the Risk of Early Warning

TAO Yong-hong^{ [1]}

QI Ai-lin**[2]**

**Abstract**: We all expect that we can predict the risk before it appears, the
risk of early-warning has become a research hotspot in many fields, so does the
economy of risk early-warning. In recent years, using Artificial Neural Network
to solve the risk of early warning problem has been developed, but the risk of
early warning process often encounters such a problem: The risk assessment has
no standard, meanwhile BP Neural Network is a kind of instructors train, and
instructors come from the standard. This paper combines Efficacy Coefficient
Method and BP Neural Network to achieve the purpose of early warning on the
economy problem, it has remedies the limitation of risk of early warning by
simply using BP neural network.

**Key
words**: Risk Early Warning; Efficiency Coefficient
Method; BP Neural Network

1. Introduction

In early-warning problem, it often
appears that the danger lines are difficulty to define. Although some methods
such as Efficacy Coefficient Method can rank the risk, because of the lag of
statistical data, ranking risk can not be reaching the purposes of early
warning. Only use trained BP neural network can be used to predict and alarm,
but because of the network belongs to guide learning, so it needs the data to
be trained with a standard
measurement, that is the ranking risk. Thus data
input can not be achieved the purpose of training the network. The combination
of two methods can complement each other, it called EC-BP.

2. Early Warning Process Based on EC-BP

First use Efficacy Coefficient
Method to evaluate the historical period risk, given an integrated early warning
score, according to the score numerical value and early warning lines of
pre-set criteria to determine risk. the calculated results as the expected
output of BP network, so as to calculate the error of the expected output and
actual output, and thus train the network to be an ideal network model, early
warn the next period. The Specific procedure as shown below:

**Fig.1.1 map of
early warning process based on EC-B**P

3． principal
component analysis process

In this paper, it calculates the
weights of various indicators by principal component analysis, different from
traditional qualitative methods to determine the weight, it can get rid of
man-made factors, starting from the data to identify the relationship between
the data, so as to determine the weight of each indicator.

Suppose there are samples taken into consideration, each
sample has observed value, the original matrix_{}, and then the calculation
represented as:

First, standardize the original data. Second, establish
correlation coefficient matrix of variables. Third, calculate the characteristic roots _{} and the corresponding unit eigenvectors. Fourth,
select _{}（_{}＜_{}）principal components, making _{}＝_{}（_{}≥85%）, select_{} as the first principal component, _{} as the second principal component, ... , _{}as the _{}th principal component. Among them,
the first principal component _{} corresponds to the characteristic root _{}, the rest and so on^{ }(L.Bobrowski, M.Topczewska, 2008). Fifth, make the
explanations to economic phenomena by selected principal component.

Calculate the sum of squares of indicators eigenvector and the weight of indicators, the weight of other indicators and so on.

_{}

_{}

Where _{}is the eigenvector of indicator_{}, _{} is the number of
indicators, _{} is the number of
principal components, _{} is the weight of indicator_{}.

4. Evaluation Process of Efficacy Coefficient Method

Efficacy coefficient method is based on multi-objective decision making theory, it ascertain a satisfactory value and unallowable value of each evaluation indicator to determine the value of each indicators to achieve satisfactory level, calculate the fraction of the indicators through satisfactory value to the ceiling and unallowable value to the lower limit. After educing weighted mean, then the situation of research objective can be evaluated.

_{}

_{}_{}

Where _{} is efficacy
coefficient of risk factor, _{} is efficacy
coefficient of the minimal value, _{} is efficacy
coefficient of the maximum value , count _{}as indicator of weight, _{} is the actual
value, _{} is unallowable
value, _{} is satisfactory
value.

Idea using Efficacy Coefficient Method to early warning of particular process is as follows:

First, select early warning lines; they are huge, great, moderate, light and no warning respectively.

Second, use hierarchical analysis or principal component analysis method to determine the weight of each early-warning indicator.

Third, set a single area of early warning indicators, and come with the weight of each early-warning indicator to determine the integrated early warning score interval.

Fourth, calculate the efficacy coefficient.

Fifth, determine the
early-warning lines basis on the efficacy coefficient and
integrated early warning score interval.

5. Early Warning Basic on Neural Network

5.1 Algorithm for the Calculation

STEP1: Initialize network, set the initial parameters of the network.

STEP2: Input learning algorithm.

STEP3: Calculate the middle layer unit output.

STEP4: Calculate the output layer unit output.

STEP5: Calculate the error between the output layer unit and the desired output.

STEP6: Adjust the connection
weights from middle layer to output layer and the off-set of output layer units^{[2]}.

STEP7: Adjust the connection weights from input layer to the middle layer and the off-set of the middle layer units.

STEP8: Update learning algorithm, if the learning algorithm is over, get to the next step, otherwise return to STEP2;

STEP9: Update learning number, if get to the maximum number of learning, then end, otherwise return to STEP2.

5.2 Error function

Suppose there are _{} samples or _{} periods of data, the network output _{} units, due to the risk of early-warning
has a time-related features, we must measure the value of
next period to give an indicator of early warning. For the risk prediction is a
time-related function, it needs to reflect the characteristic in the BP neural
network. Therefore, the efficacy coefficient of the
next period will be regarded as the current period desired output in this
article, which the error formula during the third layer of the network is:

_{}

Where _{} is efficacy
coefficient of the risk factors of the (_{})th period, _{} is f the actual
output value of samples _{}.

Error of sample _{} is represented as:

_{}

Where is the dimension of output, namely, the output quantity.

By the formula flowered the BP
network error formula is represented as^{[3]}:

_{}

The use of neural network design
model, need to select the appropriate parameters to get fast convergence and
accurate results to the desired effect.

6. Conclusions

There are many methods for the
economic early warning, such as: Autoregressive Moving Average Model, Vector
Autoregressive System, Auto Regressive Conditional Heteroscedasticity Model,
KLR and so on ^{[4],[5],[6]}. Neural network is a widely used method.
It can effectively solve most of the economic early warning. This paper
combines Artificial Neural Network and Efficacy Coefficient in practice, to
make it more practical significance. However, the features which include
convergence speed, network performance of BP Neural Network can be improved,
which is the future researchers should pay attention to.

References

L.Bobrowski, M.Topczewska. ( 2008). *Case-Based
Reasoning on Images and Signals* [M]. Heidelberg: Springer Berlin,139-141.

Simon Haykin. (2001). *Neural Networks a Comprehensive Foundation*[M].
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Feng Ding. (2006). *Neural network expert system* [M]. Beijing: Science Press, 29.

Sachs.J, Tornell A Velasco. (1996). A
Financial Crises in Emerging Markets: The Lessons of 1995[J]. *Brookings Papers on Economic Activity,* *(1)*: 147-217.

Kaminsky G L, Lizondo S, Reinhart CM. (1998). Leading indicators of currency crises[J].
*International Monetary Fund*, *(45):*1-48.

Juliana Yim, Heather Mitchell. (2005). Comparison of country risk models: hybrid
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[1]School of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang Jiangsu, 212003,China.

[2] School of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang Jiangsu, 212003,China.

* Received 23 July 2009; accepted 27 August 2009

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