應用神經網絡未來儲戶的回報率
Future Depositors Rate Of Return Applying Neural Network

伊斯蘭銀行必須執行好為了提供更好的回報補償儲戶的錢和仍然確認伊斯蘭法律的策略。本文著手確定在他們的機會最大化分配給為儲戶選擇變量的相對重要性。在這種情況下,它變得非常必要預測未來的回報率,以獲得清晰的圖象,做出準確的決定。本研究使用一些關鍵的宏觀經濟變量,比如雅加達股指(JSI),通貨膨脹率(INFR),中央銀行的利率證書(INTR),匯率(ER),流通的貨幣(麥克風)。由于這些變量具有非線性時間序列數據,用人工神經網絡(ANN)將使用反向傳播算法作為學習算法。從觀察了央行的利率證書(INTR)和流通的貨幣(MIC)可以作為領先指標面對94.95%的準確率的問題。

回報率在伊斯蘭銀行定義為將收到多少錢在伊斯蘭銀行儲戶的存款一年即等效與傳統銀行的利率。使用損益共享原則,伊斯蘭銀行必須根據預先確定的儲戶損益分享比例分享利潤或損失。所以,返回的數量將取決于性能是影響宏觀經濟的動蕩，由儲戶收到伊斯蘭銀行的盈利能力。圖1顯示了比較伊斯蘭銀行在印尼的利率和回報率,PT銀行Mandiri Syariah預計今年2007年和2008年。這個數字顯示,回報率的PT銀行Mandiri Syariah預計今年似乎如此stabil與印尼廣告和國家銀行的利率。此外,從2007年7月到2008年6月,PT Mandiri Syariah預計今年銀行為存款人然后傳統銀行提供更高的回報。

Islamic bank has to perform good strategy which still confirm with the Islamic law in order to deliver better return to compensate depositor`s money. This paper is embarked on to identify the relative significance assigned to selection variables for depositor in maximizing their opportunity. In such case, it becomes very necessary to have a prediction of future rate of return in order to get a clear picture in making precise decision. This research used some key macroeconomic variables such as Jakarta Stock Indices (JSI), inflation rate (INFR), central bank`s interest rate certificate (INTR), exchange rate (ER), and money in circulation (MIC). Since these variables are characterized as nonlinearities time series data, Artificial Neural networks (ANN) will be employed using back propagation algorithm as learning algorithm. From observation resulted that central bank’s interest rate certificate (INTR) and Money In Circulation (MIC) could be used as leading indicators to face the problem with 94.95% accuracy.

Rate of return in Islamic bank defines as how much money will be received by depositor from their deposit in Islamic bank for one year which is that equivalent with conventional bank`s interest rate. Using profit and loss sharing principle, the Islamic bank must share the profit or loss to depositors based on predetermined profit and loss sharing ratio. So, the amount of return will be received by depositor depends on Islamic bank`s profitability which performance is affected by macroeconomic turmoil. Figure 1 shows comparison between interest rate and rate of return of an Islamic bank in Indonesia, PT Bank Syariah Mandiri for period 2007 and 2008.　This figure shows that rate of return of PT bank Syariah Mandiri seems so stabil compared with interest rate of Indonesian commercials and states bank. Moreover, from July 2007 to june 2008, PT Bank Syariah Mandiri provides higher return to its depositor then conventional bank.#p#分頁標題#e#

The steady expansion of Islamic banks has been the hallmark of the Muslim world financial landscape in the 1980s and 1990s. With a network that spans more than 60 countries and an asset base of more than $166 billion; Islamic banks are now playing an increasingly significant role in their respective economies (Hassan and Bashir, 2003). As the biggest Muslim country in the world, the growth of Indonesian Islamic banking industry is still far away behind Malaysia and Turkey. Indonesian Islamic bank’s total asset accounted for USD 3.287 million compared with Malaysia and turkey, amounted to USD 34.543 million and USD 12.902 million, respectively.　

Many researches about business cycle analysis in bank industry have been conducted but then most of them have focused on the implication of the changes of the macroeconomic variables to the bank's profitability and delivering the result as recommendation to management or policy maker, especially in Islamic bank industry. [see for example, Meyer and Pifer (1970), al-Osaimy (1998), Cihak and Hesse (2008), Maximilian (2008). In contrast, this research, indeed, intends to helps depositor to understand which macroeconomic variables will significantly determine pricing of individual depositor`s rate of return in PT Bank Syariah Mandiri, the biggest Islamic bank in Indonesia and then use them to predict future rate of return.

1.1 Research Objectives——研究目標

The ability to predict future rate of return will enable depositors, especially individual depositors to take precautionary action to minimize their opportunity of loss. In this context, individual depositors might simply use some particular macroeconomic variables as indicator to predict the rate of return will be received, whether increase, decrease, or constant compared with previous period.

2. Literature review——文獻綜述

2.1 Prior Methods used to Predict Business Cycle——之前用來預測商業周期的方法

Many metholodologies have been developed on research related with business cycle analysis and prediction. Mayer and Pifer (1970) used Linear Probability Model (LPM) to predict bank failure. Al-Osaimy and Bamahramah (2004) and Cihak and Hesse (2008) used Multi Discriminant Analysis (MDA), Dewaelheyns and Hulle (2007), and Erdogan (2008), used Distributed Lag Model (DLM) and Logit. On the other hand, Kiani, Khurshid and Kasten (2006), and Hsieh, Liu and Hsieh (2006) used MDA assisted neural network to predict bankruptcy of Taiwan company. Although neural networks have demonstrated some success in this area, only a few studies, for example Al-Osaimy (1998) and Maximilian (2008) employed neural network in Islamic banking research. So, we believe conducting research in Islamic bank, might benefit from neural networks model. This research, therefore, employ the model that are considered to be highly flexible functional forms of nonlinear models to find possible predictability of Islamic bank`s business cycle, primarily on return generation ability in Indonesian Islamic bank by using a number of macroeconomic variables as independent variables since complex unstructured relationship among variables are often encountered in economics, Maximilian (2008).　#p#分頁標題#e#

2.2 Superiority of ANN method——ANN方法的優越性

Prudence (2002) declared at least two advantages of ANN method compared with other methods for doing prediction. Firstly, they are universal approximators of function in that they can approximate whatever functional form best characterizes the time series. That means, ANN are considered to be data-driven rather than model-driven (Argyrou, 2006) because they are best suited for problems for which data is available but the underlying theoretical model is unknown (Zhang, Patuwo & Hu, 1998). It makes ANN superior than other statistical methods which ANN able to deal with non linear data and multi dimensional aspect. Secondly, ANN method have been proven to be better for long term forecast horizons, but are often as good as statistical forecasting methods over shorter forecast horizons.　Atiya (2001) summarized paper of Odom and Sharda (1990) which compared forecasting power between ANN method and MDA method. ANN achieved correct classification accuracy in the range of 77.8% to 81.5% against MDA`s accuracy were in the range of 59.3% to 70.4% for predicting bankruptcy of 128 firms using financial ratios.

3.Methodology——方法論

On constructing model to answer the problem, this research used bankruptcy theory which states that probability of default of the firm is a function of macroeconomic variables such as interest rate, foreign exchange rate, growth rate, government expenses, unemployment rate, and aggregate savings (Azis and Dar, 2004). It means that the ability of the firm in generating profit is highly influenced by changes in macroeconomic condition. Using profit and loss sharing principles, the ability of Islamic bank to generate profit and share it with depositor is also influenced by macroeconomic turmoil.

Since the variables used are characterized as nonlinearities time series data, ANN model will be constructed using back propagation algorithm as learning algorithm by employing Alyuda Neuro Intelligent software version 2.2 and on a Pentium IV machine under Windows XP Professional platform.

3.1 Artificial Neural Networks Model (ANN)——人工神經網絡模型(ANN)

ANN is a branch of artificial intelligence which able to solve problem especially in pattern classification and recognition. ANN benchmark their prediction with actual results and constantly revise their predictions, improving forecasting capability (Wong, 2009). ANN modeling approach is useful for forecasters, and researchers who employ it especially in problems where data is available but the data generating process and its underlying laws are unknown. Maximilian (2008) adopted this method to modeling Islamic bank credit risk in Indonesia and concluded that ANN does overcome the problem of data sufficiency that limits many forecasting methods. ANN are treated as nonlinear, nonparametric statistical methods due to which these are independent of the distributions of the underlying data generating processes (White 1989). This research employed ANN model used by Kiani et al (2006) as can be seen below in model [1]#p#分頁標題#e#

f(x) = sig [α0+αjsig (βijxi + β0j)] + ε　…[1]

where, n is the number of hidden nodes in neural networks and k is the number of explanatory variables in the networks, sig (x) = 1/(1 + e-x ), αj represents a vector of parameters or weight that link the hidden node to output layers unit. βij (i =1,......., k); j=1,........, n) denotes a matrix of parameters from the input to the hidden layers units and ε is the error term. The error term ε can be made arbitrary small if sufficiently many explanatory variables are included and if n is chosen to be large enough. However, the model may over fit if n is too large in which in-sample errors can be made very small but out-of sample errors may be large.

3.2 Data——數據

This research attempts to use as much as possible of macroeconomic variables as input variables. However, considering availability of data and commonly used in Indonesian Islamic banking research area, this research uses some key macroeconomics variables which used by Maximilian (2008) such as JSI which issued monthly by Indonesia Stock Exchange (ISE), and INFR, INTR, ER and MIC which issued monthly by Indonesian Central Bank (BI). As output variables, the research used general (not special) rate of return for 1 month time deposit which issued by PT Bank Syariah Mandiri every month. These macroeconomic variables are incorporated in the model to be analyzed which one will be the most determinant in pricing individual depositor`s rate of return and then also to predict the future rate. For doing so, real monthly data for sixty months were collected from January 2004 to December 2008. This whole data set was then divided into three sets which 59 data used and 1 data as outlier (September 2008 was removed from the sample, table 1). The training set is a part of input dataset used for neural network training, i.e. for adjustment of network weights and the validation set is a part of data used to tune network topology or network parameters other than weights.

The software will use validation set to calculate generalization loss and retain the best network (the network with the lowest error on validation set). Meanwhile, the test set is a part of input data set used only to test how well the neural network will perform on new data. The test set is used after the network is ready (trained), to test what errors will occur during future network application.

3.3 Analysis and Prediction Process——分析和預測過程

The process of analysis and prediction can be seen in Figure 2. Each arrow connecting each node represents the information (in terms of weight) in one particular note that might influence the other node. The program puts an initial weight to each arrow which is updated during the iteration process (commonly called epoch) to arrive at the lowest prediction error of default probability as the output variable in the iteration process. The level of complexity and predictive accuracy on the model depends upon the number of nodes in the architecture, Maximilian (2008).#p#分頁標題#e#

The choice of the best neural network architecture is based on a criteria mentioned in the literature and adjusted to the case of neural networks for prediction. Simply put, the network with the best structure is the one that simultaneously fulfils all the following criteria: (1) It has the smallest training error; (2) It has the smallest test error; (3) It has the smallest difference between training and testing error and (4) It has the simplest structure. The background of using ANN in this research is that of allowing the network to map the relationships between macroeconomic variables affecting rate of return given to depositor. Once this relationship between inputs and outputs is mapped, it gives the model needed to create rate of return prediction using macroeconomic data that out of sample period which are January, February and March 2009. The accuracy will be evaluated on the basis of standard statistical measures like percentage errors, as following.

Error = (Rate of Return Act) - (Rate of Return Predict ) x 100%

(Rate of Return Actual)

for i=1,2,…., N, where N is the number of testing data points. Rate of return actual data used were also out of sample period which are January, February and March 2009. After calculating the forecast error, forecasting accuracy will be calculated as;　

Forecasting Accuracy = 100% - percentage of error in forecasting

3.4 Using Alyuda Neurointelligence——使用Alyuda Neurointelligence

Argyrou, A. (2006) describes how to run Alyuda Neurointelligence to build the model`s architecture, train and then test the models. For all dataset, the input to Alyuda Neurointelligence resembles a spreadsheet. The rate of return column was set up as output or target variables and the respective variables are categorized as input variables and designated as numerical data. The data is partitioned into training, validation and testing sets (table 1). The “date” column is included to facilitate the data partitioning; it is not part of the input to the models and plays no role in training or testing the neural networks. Subsequently, the input data must be pre-processed (i.e. rate of return and macroeconomic variables) to remove data anomalies, because such anomalies can degrade the neural-network performance. In this context, data anomalies fall into the following two categories: (1) missing values and (2) outliers (Alyuda Neurointelligence v. 2.2 User Manual). In particular, missing values are values that are not known, resulting in blank cells in the input columns. Outliers are extreme values that diverge from the majority of column data. To identify outliers, the application use the following formula for every column; mean ± standard deviation x 3.5. Consequently, for any column, a value that lies outside this range is considered to be an outlier and thereby is being removed.

The next step is “normalizing” the input data to make it suitable for neural-network processing. The “normalization” essentially transforms the input data into a new representation before a neural network is trained. Bishop (1995) offers the following three reasons for input data normalization: (1) to ensure that the size of input data reflect their relative importance in determining the required output, (2) to enable the random initialization of weights before neural network training and (3) different variables may have different units of measurements, hence their typical values may differ significantly. All the input columns are “normalized” in the same way, because they all include numerical values. Alyuda provides only one method for data normalization as follows:#p#分頁標題#e#

Y= SRmin + (X – Xmin) x SF

Where: SF=(SRmax–SRmin)/(Xmax–Xmin); Y=Normalized value; X=actual value of a numeric column; Xmin=minimum actual value of the column; Xmax=maximum actual value of the column; SF=scaling factor; Srmin=lower scaling range limit; Srmax=upper scaling range limit; [-1..1]=scaling range for input columns.

In the next step, we define the three properties before running the application. First, the logistic activation function are selected for all the neurodes regardless of the layer on which they reside. Second, the sum of squared errors is selected to minimize the output error function This is the sum of the squared differences between the actual value and the model’s output. For completeness, we restate that the neural network output falls in the range from 0 to 1 or from 0 to 100%, because of the logistic activation function. Furthermore, we run the “exhaustive search” to select the best possible architecture for the models. This process takes considerable time because it searches for the best network architecture among all possible alternatives in the specified range. Alyuda choose the best architecture for the model which is 7-17-1 that consists of one hidden layer with seventeen neurodes. In addition, the model has 5 active neurons and 2 neurons as date which plays no role in training or testing the neural networks. The output layer（Ol）has a single neurode representing the model’s numeric output.

In the pen-ultimate step, the model is trained with specific condition. The learning law is the backpropagation algorithm and both the learning and momentum rates are set at 0.1. The training stops when the model`s mean squared error reduces by less than 0.000001 or the model completes 20,000 iterations, whichever condition occurs first. All network`s parameters can be seen in the table 2 below.　Then, the model is “tested” against the testing set, resulting in their respective ex-ante prediction results. Alyuda Neurointelligence presents the results from the training and testing processes in the form of classification matrices. Finally, using out of sample data, we querying prediction of target variables from out of sample period which will be tested with actual rate of return of January, February and March 2009 to measure the model`s accuracy.

4. Results and Discussion——結果與討論

The contribution factor resulted from the network shows that the INTR and MIC ranked first and second on determination of depositor`s rate of return in PT Bank Syariah Mandiri. INFR, JSI and EXR ranked third, fourth, and fifth (table 3). The significant macroeoconomics variables resulted (INTR and MIC) are similar with condition of Islamic bank in other countries such as Bahrain, Bangladesh, Iran, Jordan, Kuwait, Malaysia, Sudan, Tunisia, Turkey and United Arab Emirates. It is reported by Ahmad and Haron (1998) which explained that interest rate and money in circulation had a significant relationship with Islamic bank`s return on capital. It means that both macroeconomic variables give significant impact on delivering return to Islamic bank`s depositor.#p#分頁標題#e#

The results of applying neural network model to do prediction based on those five variables show in general very good (table 4). The trained network was applied to the training data set and showed that its quality is outperform thorough value of Absolute Error (AE) and Absolute Relative Error (ARE).

The most generally used characteristics of continuous values are RMSE (root mean squared error), AE and ARE. RMSE and AE are absolute (independent of the output value module), ARE is relative. All these values define the deviation of the predicted output value from the desired one. ARE is an error value that indicates the "quality" of the neural network training. This index is calculated by dividing the difference between actual and desired output values by the module of the desired output value. The smaller the network error is, the better the network had been trained.　Table 5 shows the actual values of out of sample period used to query prediction result from the ANN model. Network provided 99.17% accuracy in predicting RR of January 2009.　The results were slightly decreasing when predicting February 2009 and March 2009 which are 92.79% and 92.88%, respectively. That prediction resulted from actual variables which out of period sample in this following table 6. Nevertheless, this network give satisfactory result for RR prediction of three months upcoming period for 94.95% accuracy in average.

5. Conclusion——結論

In this paper, we have specified an empirical framework to investigate macroeconomic determinants of Pricing Individual Depositor`s Rate of Return in PT Bank Syariah Mandiri. Based on the results of the empirical analysis, interest rates certificate of central bank of Indonesia and money in circulation significantly determine pricing individual depositor`s rate of return. By implication, these variables can be used by depositor as leading indicator to predict future rate of return. Therefore, in order to maximize their profit opportunity, depositor should pay considerable attention to these macroeconomic indicators. It should be considered that this paper is limited in one particular bank even though the bank is the biggest Islamic bank in Indonesia, so this result might be different when it is implemented in other Islamic bank. Through the continuous adoption and application of neural networks, this research, at least has fulfilled its primary aim of providing an indicator based to build understanding to depositor about the nature of Islamic banking which offers profit and loss sharing principles that create investment relationship. This research also indicates that an Islamic bank is not stand alone bank since economic turmoil strongly influenced its profitability.