Best Fitted Model to Forecast the Trade Balance of Malaysia by Lisawati Indah Binti Osman
Faculty of Computer Science & Mathematics
UiTM, 40450 Shah Alam, Selangor lisawatiindah178@yahoo.com ABSTRACT
The main purpose of this paper is to determine the best fitted model that will perform the forecast best in the case of Malaysia trade balance. The data used in this study is obtained from the Department of Statistics, Malaysia. The inclusion of five appropriate models in this study is purposely to examine the parameter values for comparison for error measures. Models involved are based on the Univariate Modelling Techniques; Naive with Trend Model, Single Exponential Smoothing, Double Exponential Smoothing, Holt’s Method Model and Adaptive Response Rate Exponential Smoothing (ARRES). The best parameter value obtained in this study marked as the main indicator in selecting the best fitted model; indicated by the smallest value of mean square error (MSE and MAPE). Based on the analysis, Adaptive Response Rate Exponential Smoothing (ARRES) model is the most suitable model to forecast the monthly Trade balance for Malaysia.
Keywords: Fitted Model, Forecast, Parameter Value, Univariate Modelling Techniques, MSE, MAPE
INTRODUCTION
The balance of trade is the difference between the monetary value of exports and imports in an economy over a certain period of time. A positive balance of trade is known as a trade surplus and consists of exporting more than is imported while a negative balance of trade is known as a trade deficit or, informally, a trade gap.
The balance of trade forms part of the current account for a particular country, which also includes other transactions such as income from the international investment position as well as international aid. A surplus in current account shows the country's net international asset position increases correspondingly. Equally, a deficit decreases the net international asset position.
International trade plays a large role in Malaysian economy; a contributing factor to the economic gross for the country. The international trade of Malaysia consists of wide range of products. Malaysia is one of the top exporters of manufactured products; electrical and electronics, agriculture products; palm oil and other vegetables oil, mining products; crude petroleum and other products as well. The country mainly imports: electronics, machinery, petroleum products, plastics, vehicles, iron and steel products and chemicals. Malaysia’s main trading partners are United States, European Union, Singapore, Japan and China.
This paper is divided into several sections; begins with the introduction, followed by objectives of the study and methodology. In methodology section, five univariate forecasting models were evaluated to obtain the parameter values. Furthermore, the evaluation and estimation procedure will be briefly described in the same section. The section then continues with results & discussions and conclusion before end up with the references.
OBJECTIVE
The main objective highlighted in this study is to find the best fitted model that would perform the forecast best for Malaysia trade balance. The criterion involved in the selection of best model should be cautiously defined and evaluate to avoid wrong selection of forecasting models.

METHODOLOGY
The initial study of the data is crucial in determining the existence of trend, cyclical, seasonal and irregular components; where possible these components need to be calculated and isolated. Cyclical variation in time series data refer to the rises and falls of the series over unspecified period of time. The data with the cyclical component will show a cyclical pattern that wind around the linear trend. Two methods used to identify the cyclical component; Residual method and Relative Cyclical Residual Method. The formula is written as follow: and , respectively.
The technique applied to analyze selected data obtained from the Department of Statistics of Malaysia is briefly described in this section. A Univariate model is a method for analyzing data on a single variable at a time. The application of single variable model in the study provides simplicity advantage. The models were fitted into the data to obtain parameter value for comparison; main indicator for best model to predict future values of trade balance based on past observations in a given time series.
Analysis was done using five types of forecast models, which is Naive with Trend Model, Single Exponential Smoothing, Double Exponential Smoothing, Holt’s Method Model and Adaptive Response Rate Exponential Smoothing (ARRES). The statistical test and data analysis were done through Microsoft Excel. a. Naive with Trend Model
This model implies that all future forecasts can be set to equal the actual observed value in the most recent time period multiplied by the growth rate. The trend value is measured by, where is the actual value at time and is the actual value in the preceding period. If is greater than then the trend is upward and conversely if is less than then the trend is downward. Therefore, the one-step-ahead forecast is represented as, = .
This model is highly sensitive to the changes in the actual values. A sudden drop or sharp increase in the values will severely affect the forecast. Furthermore, fitting this model type will result in the loss of the first two observations in the series. On the other hand, this model is only suitable to be used for short time series. b. Single Exponential Smoothing
It is a simplest form of model within the family of the exponential smoothing techniques. It requires only one parameter, which is the smoothing constant,. The general equation for single exponentially smoothed statistic is given as, = +, where is the single smoothed value in period for is the actual value at time, represent smoothing constant, is the forecast or smoothed value for period .
There are several limitations for single exponential technique. It is best to be used in situation where data series has no significant trend, no seasonality pattern and any other underlying pattern. Furthermore, any forecast value generated beyond one step ahead is the same to the value of one-step-ahead forecast. c. Double Exponential Smoothing
This technique is also known as Brown’s method. It is useful for series that exhibit a linear trend characteristic. The following notations are used:
Let, be the exponentially smoothed value of at time and be the double exponentially smoothed value of at time. Generally, there are four equations involved.
Equation 1: Computes the single exponentially smoothed value

Equation 2: Computes the double exponentially smoothed value
=
Equation 3: Computes the difference between the exponentially smoothed values

Equation 4: Computes the adjustment factor

Forecasting for m-step-ahead are computed using the equation

where is the m-step-ahead forecast at period m made in period for
The main advantage of the double exponential smoothing method over single exponential is its ability to generate the one, two, three and so forth ahead-forecast values but this model difficult to determine the size of. The criterion is to choose such that the MSE is minimum. However, it can be ease by using ‘solver’ in Microsoft excel to find the best parameter value. d. Holt’s Method

Holt’s Method is a technique that takes into account to smooth the trend and the slope directly by using different smoothing constants. It also provides more flexibility in selecting the parameter value which the trend and slopes are tracked. Holt’s Method consists of three basic equations that define the exponential smoothed series and the trend estimate. The Holt’s Method equations are represented as follows:
Exponentially smoothed series:

Trend estimate:

Therefore, the one-step-ahead forecast is:

Where, = exponentially smoothed series, = actual values, = trend estimate = smoothing constant and = smoothing constant for the trend estimate e. Adaptive Response Rate Exponential Smoothing (ARRES)
ARRES technique is incorporating the effect of the changing pattern of the data series into the model. It comprises of the following basic equation. For the one-step-ahead forecast;

The values of where, ; , and that,
The value of is defined as the smoothed average error, and is the smoothed absolute error. In the application of this model, there is no best value for because there is no single best value which happens to vary overtime.
Initial Values of the Model
As any exponential smoothing technique, ARRES model requires the appropriate initial values to start the algorithm. In this case, values are for,, and .
First, the arbitrary values for and were selected and that the initial value for the estimate for M1,2008, , be equal to the actual for M1,2008, ; in other words, . This means that error, is set to zero and that the initial values for and are also set to zero. Note that the value of must not exceed 1. Different values of and were experiment to see the differences in the results. Solver application is also used to determine the optimum initial values.
Estimation and Evaluation Procedures
Basically, there are three stages involved in this procedure: i. In the first stage, the data series is divided into two parts. The first part is called model estimation part (or fitted part) and the second part is the evaluation part (or holdout part), which will be used to evaluate the model’s forecasting performance; ii. In the estimation part, the five models were fitted into the data. The minimum value of and are determined by ‘Solver’ facility available in Microsoft Excel which derived parameter values from data series for the related models. The model with the smallest MSE will be selected in this part. iii. In the evaluation part, the process in stage two was repeated again but this time, each model was compared based on the MSE and MAPE value. The model with the smallest MSE and MAPE value will be selected as the best fitted model for forecasting.
RESULTS AND DISCUSSION
Univariate forecasting model was used to predict trade balance for the first month of year 2011 in Malaysia. The estimation was done by using data from first month of 2008 to the third month of 2010, while remaining observations from the fourth month of 2010 to the twelfth month of 2010 were used to evaluate model forecasting performance. Malaysia trade balance (Billion) for the period of study from the first month of 2008 to the twelfth month of 2010 is shown in Table 1(refer to Appendices).
The initial study of the data is crucial in determining the existence of trend, cyclical, seasonal and irregular components. Base on the figure 1 below, the data shows the existence of the cyclical component since it shows a cyclical pattern that wind around the linear trend.
Figure 1 shows the graph and the trend line of the trade balance from the first month of 2008 to the twelfth month of 2010. Values of trade balance indicate a maximum increase during the third to fifth month of 2008, with 15.47590 billions, before it begins to decrease and increase steadily until the third month of 2010. The trade balance then experience a steep decrease during the third to sixth month of 2010 with 14.32700,9.25490 8.12790 and 6.04320 (billions) respectively before continuing to fluctuates back until the end of 2010.The overall trend line equation for quarterly data is given by. The trend line indicates that the underlying pattern of the data follows a relatively stable downward trend.
Figure 1: Monthly Balance Trade, Malaysia, M1,2008-M12,2010

Univariate Modelling Techniques
The estimations were done with the objective of minimizing MSE and MAPE for both in the estimation and evaluation part. Graphs for each model and results of the corresponding MSE and MAPE value for each model are shown below. i. Naive with Trend Model
Figure 2: Fitted Naive with Trend Model, Malaysia, M1,2008-M12,2010

Table 3: MSE and MAPE for Naïve with Trend Model

ERROR MEASUREMENT | MSE | MAPE | Evaluation Period: (M4,2010-M12,2010) | 18.03227 | 0.667862 | Evaluation Period: (M4,2010-M12,2010) | 11.16991 | 1.241101 |

ii. Single Exponential Smoothing
Computation of the minimum value of α was determined by solver facility available in Microsoft Excel. Based on the solver result, the best α to use is 0.530030776 since it minimizes the error measure.
Figure 3: Fitted Single Exponential Smoothing Model, Malaysia, M1,2008-M12,2010

Table 4: MSE and MAPE for Single Exponential Smoothing Model

ERROR MEASUREMENT | MSE | MAPE | Evaluation Period: (M4,2010-M12,2010) | 4.901155 | 16.19106 | Evaluation Period: (M4,2010-M12,2010) | 4.940316 | 23.85486 |

iii. Double Exponential Smoothing
Computation of the minimum value of α was determined by solver facility available in Microsoft Excel. Based on the solver result, the best α to use is 0.5 since it minimizes the error measure.
Figure 4: Fitted Double Exponential Smoothing Model, Malaysia, M1,2008-M12,2010

Table 5: MSE and MAPE for Double Exponential Smoothing Model
ERROR MEASUREMENT | MSE | MAPE | Evaluation Period: (M4,2010-M12,2010) | 4.881479 | 16.06991 | Evaluation Period: (M4,2010-M12,2010) | 5.017339 | 24.28515 |

iv. Holt’s Method Model
Like previous model, the computation of the minimum value of α and β was determined by solver facility available in Microsoft Excel. Based on the solver result, the best α= 0.530030776, β= 0.1since it minimizes the error measure.
Figure 5: Fitted Holt Method Model, Malaysia, M1,2008-M12,2010

Table 6: MSE and MAPE for Holt’s Model

ERROR MEASUREMENT | MSE | MAPE | Evaluation Period: (M4,2010-M12,2010) | 5.199978 | 16.67829 | Evaluation Period: (M4,2010-M12,2010) | 5.798515 | 24.20127 |

v. Adaptive Response Rate Exponential Smoothing (ARRES)
There is an exceptional case for ARRES model, where there is no best parameter estimate. Therefore, the computational of the minimum value of α and β was determined by solver facility available in Microsoft Excel. Based on the solver result, α= 0.1, β= 0.6 will be the optimum initial values.
Figure 6: Fitted Adaptive Response Rate Exponential Smoothing (ARRES), Malaysia, M1,2008-M12,2010

Table 7: MSE and MAPE for Adaptive Rate Exponential Smoothing (ARRES) Model
ERROR MEASUREMENT | MSE | MAPE | Evaluation Period: (M4,2010-M12,2010) | 4.8871271 | 17.578405 | Evaluation Period: (M4,2010-M12,2010) | 4.7886913 | 22.571628 |

Error comparison and model selection
Table 8: MSE Value comparison for each model
Table 8 presents the summaries and comparison on MSE figures for ; Naive with Trend Model, Single Exponential Smoothing, Double Exponential Smoothing, Holt’s Method Model and Adaptive Response Rate Exponential Smoothing (ARRES). Based only on the MSE value calculated over the fitted period, it can be concluded that the most suitable model to forecast the balance trade is Double Exponential Smoothing Method with α = 0.5 since it has the smallest value of MSE compared to other forecasting techniques.

| | | | Model Types | | | Time Series | Error Measures | Naive with trend method | Single Exponential Smoothingα= 0.530030776 | Double Exponential Smoothingα= 0.5 | Holt’s Modelα= 0.530030776, β= 0.1 | ARRESα= 0.1, β= 0.6 | Estimation Period:(M1:2008-M3:2010) | MSE | 18.03227 | 4.90116 | 4.88148 | 5.19998 | 4.88713 |

Table 9 presents the summaries and comparison on MSE and MAPE figures for ; Naive with Trend Model, Single Exponential Smoothing, Double Exponential Smoothing, Holt’s Method Model and Adaptive Response Rate Exponential Smoothing (ARRES). Based on the MSE value calculated over the evaluation period, it can be concluded that the most suitable model to forecast the balance trade is ARRES method with α = 0.1 and β = 0.6 since it has the smallest value of MSE compared to other forecasting techniques.

| | | | Model Types | | | Time Series | Error Measures | Naive with trend method | Single Exponential Smoothingα= 0.530030776 | Double Exponential Smoothingα= 0.5 | Holt’s Modelα= 0.530030776, β= 0.1 | ARRESα= 0.1, β= 0.6 | Evaluation Period:(M4:2010-M1:2010) | MSE | 11.16991 | 4.94032 | 5.02913 | 5.79852 | 4.78869 | | MAPE | 30.54878 | 23.85486 | 24.31383 | 24.20127 | 22.57164 |
Table 9: MSE and MAPE Value comparison for each model

CONCLUSION
Based on the one-step-ahead forecast analysis, Adaptive Response Rate Exponential Smoothing (ARRES) model is the most suitable model to forecast Malaysia monthly trade balance. This is because; Based on the evaluation part the model shows the smallest MSE and MAPE value; 4.78869 and 22.57164 respectively. The model forecasted the trade balance to reach 9.536881243 billion for the first month of 2011. Univariate Modelling Techniques are basically single variable models that use their past information as the basis to generate the forecast values. This is made on the assumption that the forecast values are dependent solely on the past pattern of the data series. However, in forecasting for longer term, it is less statistically fit than the one-step-ahead forecast because the more recent data may depart from the previous underlying process.

International trade plays a large role in Malaysian economy; a contributing factor to the economic gross for the country. Therefore, the forecasting of balance trade should become one of the major fields of research in recent years to provide any particular country with the clear picture of their performance in terms of economic sector. .

REFERENCES
Malaysia Export By Products Statistics 2001 (January), n.d retrieved October 15, 2011, from http://e-directory.com.my/doc/info-export%20by%20products.htm
Lazim, M. A. (2011). Introductory Business Forecasting A Practical Approach. Third edition, University Publication Center (UPENA), Universiti Teknologi Mara, Shah Alam.
Liang, H. S et.all. Real Exchange Rate and Trade Balance Relationship: An Empirical Study on Malaysia. Vol. 3, No. 8.
Fengbao Y. et.all. The Sustainability of Trade Balances in China. Kobe University.Volume 31, Issue 3

M. Faruk Aydın, et.all, Export Supply and Import Demand Models for the Turkish Economy, No:04/9

Falk, M.Determinants of the Trade Balance in Industrialized Countries, 2008