Because the volume of currency issued by a country always affects its interest rate, price index, income levels, and many other important macroeconomic variables, the prediction of currency volume issued has attracted considerable attention in recent years. In contrast to the typical singlestage forecast model, this study proposes a hybrid forecasting approach to predict the volume of currency issued in Taiwan. The proposed hybrid models consist of artificial neural network (ANN) and multiple regression (MR) components. The MR component of the hybrid models is established for a selection of fewer explanatory variables, wherein the selected variables are of higher importance. The ANN component is then designed to generate forecasts based on those important explanatory variables. Subsequently, the model is used to analyze a real dataset of Taiwan's currency from 1996 to 2011 and twenty associated explanatory variables. The prediction results reveal that the proposed hybrid scheme exhibits superior forecasting performance for predicting the volume of currency issued in Taiwan.
The Central Bank of Taiwan is responsible for planning and producing the currency of the country. The volume of currency issued is primarily determined by the demand of the public. It is associated with the economic growth rate, seasonal factors, and the development of noncash payments. Because the issue of currency is very important from an economic point of view, the prediction of currency volume issued has become an important research topic [
In contrast to the error correction model (ECM) for predicting the volume of currency issued [
The second proposed technique is the twostage hybrid modeling scheme. The general concept of using a hybrid scheme is to capture different patterns in the data by taking advantage of each individual model’s capability. The research findings indicated that the hybrid modeling is superior for improving the performance of each individual model [
This hybrid model is then used to analyze a real monthly dataset containing one response variable (i.e., Taiwan’s currency) and twenty associated explanatory variables obtained from January 1996 to December 2011. The real dataset makes it possible to compare predictions about Taiwan’s currency using the singlestage models and twostage hybrid models. This study applies the first 14 years of data to build the forecasting models and then performs a confirmation test using the last two years of data. The rest of the study is organized in the following manner. Various forecasting methodologies are discussed in Section
In this study, we employ singlestage forecasting techniques, ARIMA, MR, and ANN, as well as a twostage hybrid technique, MRANN, to predict the volume of currency issued. Additionally, to compare the performance of the different performance models, a real Taiwanese currency dataset is analyzed. The dataset consists of 192 records. Each sample record consists of 20 variables that are summarized in Table
Explanatory variable definitions in the dataset.
Variable  Meaning 


Issued currency 

Stock price index 

Total trading value on the stock market 

Total trading value on the bond market 

Total trade value on call loan 

Interbank closing spot exchange rate (NT$/US$) 

The price of gold 

Annual growth rate of consumer prices 

Annual turnover rate of checking accounts 

Number ratio of dishonored checks 

Foreignexchange reserves 

Discount rate 

Interest rate of accommodations with collateral 

1month deposit rates 

1year deposit rates 

Interbank call loan market interest rate 

Cp rates 

Deposits of major financial institutions 

Amount outstanding of bond market 

Unemployment rate 

Month of lunar new year 
The time series data can be simply defined as observations made in a sequential order. Because seasonal effects are involved in the prediction of the currency issued, time series forecasting techniques should be used. Box and Jenkins [
A general ARIMA model can be described as follows:
Typically, the original time series (i.e.,
In recent years, ANN has been widely applied in engineering, education, social science, medical research, business, and forecasting. A neural network is a massively parallel system comprised of highly interconnected, interacting processing elements based on neurobiological models [
ANN can be classified into two categories: feedforward and feedback networks [
The generalized delta rule is the conventional technique used to derive the connection weights of the feedforward network [
Regression analysis is one of the most used statistical methods in modeling realworld applications. The modeling process involves setting up the relationships between one dependent (or response) variable and several independent (or explanatory) variables. The performance of the regression models is typically acceptable as long as the assumptions have been met. However, the assumptions of the regression model (e.g., variation homogeneity) often confine its application.
The general MR model can be represented as follows:
the
the
the variance of
the values of
Because collinearity among independent variables will lead to imprecise estimates and serious stability problems, the collinearity diagnosis procedure should be performed first before screening significant independent variables. Some wellknown criteria such as the variance inflation factor (VIF) or tolerance can be applied to examine collinearity. The VIF is defined as follows:
In addition, when a large number of explanatory variables are involved in the MR design, a great amount of computation is required for examining a large volume of computer outputs, most of which is associated with poor MR models. As a consequence, three variable selection procedures are employed in this study. Those three selections include forward selection, backward elimination, and stepwise regression procedures. Given a dataset with twenty explanatory variables, this study uses those three selection procedures to determine the explanatory variables that lead to the best model. The selection procedures are iterative, wherein a single explanatory variable is added or deleted at each step of the procedure, and the new model is evaluated. The criterion for selecting an explanatory variable is based on
After performing various modeling techniques to predict the Taiwan’s currency, the results are reported and discussed in this section.
For the ARIMA modeling, this study divides the currency data into two groups. The first group contains 168 samples used for the design of the model, and the second group contains 24 samples used for the confirmation of the model. Figure
Time plot for currency issued in Taiwan (unit: 10^{8} NT$).
After performing the identification, estimation and diagnostic assessment steps using the SAS package, we obtain the parameter estimates provided in Table
Parameter estimates for the time series model.
The ARIMA procedure  

Conditional least squares estimation  
Parameter  Estimate  Standard error 

Approx. 
Lag 
MA1,1  0.59010  0.06694  8.82  <.0001  1 
AR1,2  −0.83540  0.07871  −10.61  <.0001  12 
AR1,3  −0.60107  0.08684  −6.92  <.0001  24 
Autocorrelation test for residuals for the ARIMA model.
To lag  Chisquare  DF  Pr > ChiSq  Autocorrelations  

6  1.19  2  0.5512  −0.048  0.039  0.022  0.049  0.019  0.018 
12  6.30  8  0.6141  0.046  −0.010  0.019  0.086  0.092  0.108 
18  14.87  14  0.3871  0.216  0.028  0.021  0.045  0.002  0.006 
24  22.11  20  0.3344  0.028  −0.005  −0.024  0.006  0.194  −0.018 
30  23.62  26  0.5979  0.086  0.001  0.012  −0.014  −0.015  −0.002 
36  24.85  32  0.8121  −0.020  −0.020  −0.015  −0.063  0.029  0.017 
The purpose of using ANN is to predict the currency issued in Taiwan. The structure of the ANN is described as follows. It has been reported that more than 75% of neural networks applications use the backpropagation neural network (BPNN) structure. Thus, this study uses the BPNN in designing the ANN forecasting model [
After performing the ANN modeling, we found that the
The topology setting results for ANN model alone.
ANN alone  

ANN topology  MAPE 
{20181}  6.634 
{20191}  5.876 
{20201}  5.534 
{20211}  5.940 
{20221}  6.833 
This study considers currency issued (i.e.,
Pearson correlations for pairs of variables.




















 


1.00  

0.69  1.00  

−0.27  −0.16  1.00  

0.33  0.11  0.17  1.00  

−0.46  −0.12  0.41  −0.17  1.00  

0.30  0.10  0.05 

−0.18  1.00  

0.19  −0.13  0.01  0.00  −0.43  0.06  1.00  

−0.12  0.04  −0.38  −0.66  0.07  − 
−0.08  1.00  

−0.06  −0.06  −0.53  −0.61  −0.27  − 
0.08 

1.00  

0.19  0.06  0.38 

−0.01 

0.04 


1.00  

0.29  0.12  −0.56  −0.43  −0.43  −0.54  0.28 



1.00  

0.29  0.12  −0.56  −0.43  −0.43  −0.54  0.28 




1.00  

0.20  0.10  −0.58  −0.50  −0.32  −0.65  0.18 





1.00  

0.20  0.07  −0.59  −0.49  −0.40  −0.63  0.21 






1.00  

0.20  0.13  −0.56  −0.53  −0.31  −0.67  0.14 







1.00  

0.20  0.11  −0.58  −0.50  −0.33  −0.64  0.15 








1.00  

0.15  0.07  0.37 

0.13 

−0.04 









1.00  

0.07  0.02  0.52  0.70  0.16 

0.01 



− 






1.00  

−0.38  −0.13  0.36  0.36  0.50  0.48  −0.38  −0.54  − 
0.62 






0.68  0.69  1.00  

−0.03  −0.19  −0.12  −0.14  −0.02  −0.02  0.16  −0.04  0.00  −0.02  0.01  0.01  0.00  0.01  0.02  0.03  −0.02  −0.02  −0.04  1.00  

0.27  0.08  0.21 

−0.10 

0.09 



−0.59  −0.59  −0.69  −0.67 

−0.68 


0.46  0.23  1.00 
The results of parameter selection using VIF.
Coefficient estimates  VIF  

Constant  583375011.42 


6158.38  3.101 

476.78  2.477 

−239.34  1.675 

−4071362.58  1.899 

−1672867.30  1.458 

1897.76  1.349 

182059933.71  1.111 
After using VIF to perform the parameter selection, this study used the typical statistical hypothesis tests to obtain the significant variables in the model. Accordingly, this study deleted the variables from seven retained variables (i.e.,
The results of parameter estimates using the significance tests.
Coefficient estimates 

Significance  

Constant  515251473.83  44.42828  0.000 

−258.41  −3.2937  0.001 

1819.38  24.76641  0.000 

188422296.76  10.80766  0.000 
This study also used three selection techniques to develop the MR models for the currency issued. These three techniques include forward selection, backward elimination, and the stepwise regression analysis.
The concept of three variable selection procedures is described as follows. The forward selection is similar to the stepwise selection. The first explanatory variable selected for inclusion of the regression equation is the one with the largest positive or negative correlation with the dependent variable,
In our experiment, all those three selection procedures resulted in the same MR model. Table
The results of parameter estimates using the three selection procedures.
Coefficient estimates 

Significance  

Constant  450609032.27  17.169  0.000 

9385.75  2.733  0.007 

−192.95  −2.394  0.018 

1786.46  24.453  0.000 

191890298.23  11.191  0.000 
In our proposed twostep hybrid model, the first step is to obtain the appropriate input variables for the ANN model. Because this study utilizes different MR modeling selections, the explanatory variables in MR_{VIF}, MR_{SIG}, and MR_{SEL} models serve as the input variables for ANN. Accordingly, this study employs three combinations of MR and ANN as the candidate hybrid models, wherein combinations of MR_{VIF} and ANN, MR_{SIG} and ANN, and MR_{SEL} and ANN are referred to as MR_{VIF}ANN, MR_{SIG}ANN, and MR_{SEL}ANN, respectively.
When the first stage of hybrid modeling is completed, the ANN topology settings are established. Table
The ANN topology setting for hybrid models.
MR_{VIF}ANN  MR_{SIG}ANN  MR_{SEL}ANN  

ANN topology  MAPE  ANN topology  MAPE  ANN topology  MAPE 
{751}  4.272  {311}  3.622  {421}  4.135 
{761}  3.576  {321}  3.785  {431}  3.801 
{771}  3.603  {331}  4.453  {441}  3.659 
{781}  4.073  {341}  3.859  {451}  3.526 
{791}  3.530  {351}  3.620  {461}  3.672 
This study develops various forecasting models to predict the volume of currency issued in Taiwan. Table
Performance comparison of hybrid and singlestage models.
MAPE  RMSE  MAD  

Singlestage models  
ARIMA  5.561  90211779  70983810 
ANN  5.534  99438863  71830752 
MR_{SIG}  4.291  662791312  395781618 
MR_{SEL}  4.172  666308675  398221374 
Proposed hybrid models  
MR_{VIF}ANN  3.530  84906894  47388848 
MR_{SIG}ANN  3.484  83240416  46661477 
MR_{SEL}ANN  3.459  83909091  46313136 
Nevertheless, our proposed hybrid models provide more accurate results than the singlestage models. In terms of MAPE, MSE or MAD, the three hybrid models are all lower than the four singlestage models. The MAPE percentage improvements of the proposed MR_{VIF}ANN model over the four single stage models, ARIMA, ANN, MR_{SIG}, and MR_{SEL} for the 24period forecasts are 36.52%, 36.21%, 17.73, and 15.39%, respectively. Table
Improvement of the proposed models in comparison with the singlestage models.
Models  MAPE (%)  RMSE (%)  MAD (%) 

Proposed hybrid MR_{VIF}ANN model  
ARIMA  36.52  5.88  33.24 
ANN  36.21  14.61  34.03 
MR_{SIG}  17.73  87.19  88.03 
MR_{SEL}  15.39  87.26  88.10 
Proposed hybrid MR_{SIG}ANN model  
ARIMA  37.35  7.73  34.26 
ANN  37.04  16.29  35.04 
MR_{SIG}  18.81  87.44  88.21 
MR_{SEL}  16.49  87.51  88.28 
Proposed hybrid MR_{SEL}ANN model  
ARIMA  37.80  6.99  34.76 
ANN  37.50  15.62  35.52 
MR_{SIG}  19.39  87.34  88.30 
MR_{SEL}  17.09  87.41  88.37 
The accurate prediction of currency volume issued is very important for the economic development of a country. This study performed a comparison of singlestage and hybrid models in predicting the volume of currency issued in Taiwan.
Because it is difficult to fully capture the characteristics of the real data, the hybrid scheme can be a good practical modeling approach. In this study, the concept of the proposed hybrid scheme takes advantage of each component model’s unique capability to capture patterns in the currency data. Different combinations of hybrid technique were proposed to overcome the deficiencies of single models and yield more accurate prediction results. In this study, the MAPE, MSE, and MAD are used to measure the forecasting capability. The forecasting results reveal that the hybrid models are more fruitful methods for improving the forecasting performance of each singlestage model.
The proposed hybrid technique is more effective than the singlestage modeling. However, due to the difficulty of obtaining other countries’ datasets, we are unable to perform the same procedures in reference to other countries. We do believe that the proposed hybrid approach is suitable for forecasting the currency issued for other countries in addition to Taiwan. We have described a framework for integrating several frequently used MR modeling methods and ANN techniques. The extension of these twostage hybrid procedures to other techniques is currently under investigation.
This research was supported in part by the National Science Council of Taiwan, Grant no. NSC 992221E030014MY3.