**Forecasting Malaysian Ringgit Using Exponential Smoothing Techniques**
**\*1Noreha Mohamed Yusof,** **2Norani Amit,** **3Nor Faradilah Mahad, 4Noorezatty Mohd Yusop**
1,2,4 Center of Statistical and Decision Science Studies
**Faculty of Computer and Mathematical Sciences**
**Universiti Teknologi MARA Cawangan Negeri Sembilan**
Persiaran Seremban Tiga/1, Seremban 3, 70300 Seremban,
Negeri Sembilan, Malaysia.
3 Center of Mathematical Studies
**Faculty of Computer and Mathematical Sciences**
**Universiti Teknologi MARA Cawangan Negeri Sembilan**
Persiaran Seremban Tiga/1, Seremban 3, 70300 Seremban,
Negeri Sembilan, Malaysia.
Corresponding author: \*noreh144@uitm.edu.my
Received Date: \*date
Accepted Date: \*date
Published Date: \*date
**HIGHLIGHTS**
- The exchange rate of Malaysian Ringgit (MYR) against USD for 5 years period starting from August 2013 to July 2018 was extracted from Investing.com.
- There are three methods used in this paper which are Single Exponential Smoothing, Double Exponential Smoothing, and Holt’s Method.
- Error measure which is Mean Square Error is used to differentiate between a poor forecast model and a good forecast model.
ABSTRACT
*Forecasting the foreign currency exchange is a challenging task since it is influenced by political, economic and psychological factors. This paper focuses on the forecasting Malaysian Ringgit (MYR) exchange rate against the United States Dollar (USD) using Exponential Smoothing Techniques which are Single Exponential Smoothing, Double Exponential Smoothing, and Holt’s method. The objectives of this paper are to identify the best Exponential Smoothing Technique that describes MYR for 5 years period and to forecast MYR 12 months ahead by using the best Exponential Smoothing Technique. The comparison between these techniques is also made and the best one will be selected to forecast the MYR exchange rate against USD. The result showed that Holt’s method has the smallest value of error measure which depending on the Mean Square Error (MSE) for the evaluation part. The MSE is 1.43915x10-14. Meanwhile, the forecast value of MYR in August 2019 is RM 4.30226.*
*Keywords: exponential smoothing techniques, forecasting, univariate model.*
# INTRODUCTION
The foreign exchange rate between two currencies is the rate at which one currency will be exchanged for another and it is determined by supply and demand factor (Das, Mishra, & Rout, 2017) and not all currency pairs are the same. Thus, all currency has its own buy price and a sell price with exchanging currencies at a current determined price. The need to use a good exchange rate forecasting method is crucial. This is because a currency can rise in value (appreciate or revalue) or decline in value (depreciate or devalue) in relationship to other currencies (Frieden, 2015). As of 27th May 2019, the ringgit opened marginally higher and rose to 4.1850/1900 against American Dollar (USD) compared with 4.1870/1900 at last 24th May 2019 close on improved oil prices, recovering some demand for the ringgit. The ringgit however traded lower against major currencies such as Singapore dollar, Japanese yen, British pound, and euro (Bernama, 2019).
The currency crash can be caused by an exogenous factor which is an unpredictable non-economic reason such as wars, natural disasters, political actions, and endogenous factors due to the great complexity of the system (Egorova, & Klymyuk, 2017). Thus, forecasting the foreign exchange rates is a rather complex, challenging, and difficult task since it is influenced by economic, political, and psychological factors. Economists and investors forecast the exchange rates to exploit the predictions to derive monetary values (Bui, Truong Vu, & Huong Dinh, 2018).
# LITERATURE REVIEW
Many research related to time series data forecast has been conducted as an attempt to predict the future based on the scientific method (Fauziah, Aris, Sari, & Titi, 2017).. In decades, time series models have been applied in many areas including forecasting exchange rates (Maria, & Eva, 2011; Valakevicius, & Brazenas, 2015). Different approaches have been discussed to forecast the exchange rate of MYR against other currencies. For instance, a study had proved the relevance of using the Smooth Transition Autoregressive (STAR) non-linear model and the conventional linear Autoregressive (AR) time series model for forecasting MYR/Yen series (Liew, & Ahmad Zubaidi, 2002). Findings showed that the non-linear model, STAR performed better than the linear model, AR. On the other hand, hybrid ARIMA-GARCH and hybrid ARIMA-EGARCH models were employed to forecast daily data of the USD exchange rate against MYR (Mustafa, Ahmad, & Ismail, 2017). The volatility and leverage effect of the series fitted and performed better by ARIMA-EGARCH. Furthermore, a study on forecasting exchange rates of MYR against Great Britain Pound (GBP) showed that the Exponential Smoothing method can produce better forecasting for the short forecasting period (Wan Ahmad, & Ahmad, 2013).
During the earlier studies of the time series model, researchers proved that random walk based models performed better than the use of macroeconomics indicators in forecasting exchange rates Meese, & Rogoff, 1983). However, studies on the performance of non-parametric and parametric models on a long term series of the exchange rate found that the efficiency will be lost for a time horizon of more than a year (Chinn, & Meese, 1995; Mark, 1995). . Random walks model is said to perform better in short term series and will lose its superiority when the time horizon was increased to more than 3 years. Besides, many researchers agreed that the exchange rate was difficult to track due to some reasons such as poor forecasting performance caused by nonlinear series and fundamental predictors do not always contribute significantly to the variability of exchange rates (Sarno, 2000; Groen, 2000).
A good model to use on any time series data depends on factors such as simplicity, accuracy, and stability (Gooijer, & Hyndman, 2006; Osarumwense, 2014). In many years, various forecasting methods from different fields and applications have been proposed. Models such as Exponential, Holt-Winters models or linear regression has been proven to provide a simple and comprehensive solution to forecasting time series data. In univariate time series, exponential smoothing methods suggested by Brown (Brown, 1959) and Holt (Holt, 1957) is widely used because of its simple and robust forecasting procedures (Vallet, Bermudes, & Vercher, 2011). The methods can track the trends or seasonality component from irregular variation. It is effectively used while using time series components that change slowly over time (Zhi-Peng, Hong, Yun-Cai, & Fu-Qiang, 2008). Generally, exponential smoothing is inexpensive techniques that produce good forecast in extensive applications. In advantage, low data storage and computing requirement are needed by this method which suits the real-time application (Yaffee, & McGee, 2000).
Meanwhile, the Holt-Winters method (additive Holt-Winters and multiplicative Holt-Winters) was proposed by Winters (Winters, 1960), popularized for seasonal time series (Koehler, Snyder, & Ord, 2001). The formulation is based on the assumption that every time series came from the Holt-Winters model are sharing a common structure, smoothing parameters, and corresponding errors in the univariate models are correlated (Vallet, Bermudes, & Vercher, 2011).
There are two objectives of this paper. The first objective is to identify the best Exponential Smoothing Technique that describes Malaysian Ringgit (MYR) for 5 years period. The data about the exchange rate of Malaysian Ringgit (MYR) against USD for 5 years period starting from August 2013 to July 2018 was extracted from Investing.com and used in this paper. The second objective is to forecast MYR 12 months ahead by using the best Exponential Smoothing Technique.
# METHODOLOGY
**There are three methods used in this paper which are Single Exponential Smoothing, Double Exponential Smoothing, and Holt’s Method.**
**Single Exponential Smoothing**
This model is the simplest form of the model within the family of the exponential smoothing technique. The model requires only one parameter, which is the smoothing constant, α, to generate the fitted values and hence forecast. The advantage of this procedure over the moving average is that it takes into account the most recent forecasts.
General equation
(1)
where,
is the single exponentially smoothed value in period *t*+*m* (this is also defined as forecast value when generated out-of-sample), for *m* = 1, 2, 3, 4,…
is the actual value in period *t*
is the unknown smoothing constant to be determined with value lying between 0 and 1,
i.e. (0 ≤ *α* ≤ 1), selected by the forecaster or alternatively determined by the data
is the forecast or smoothed value for period *t*.
**Double Exponential Smoothing**
This technique is also known as Brown’s Method. This method is useful for series that exhibits a linear trend characteristic. The following are four main equation used in this method
> (2)
>
> (3)
>
> (4)
>
> (5)
>
> (6)
where,
be the exponential smoothed value of *yt* at time *t*
be the double exponentially smoothed value of *y*t at time *t*
is the forecast for period t for m=1,2,3,4…
**Holt’s Method**
Holt’s two parameter method is used to handle data with a linear trend was developed. This technique not only smoothes the trend and the slope directly by using different smoothing constants but also provides more flexibility in selecting the rates at which the trend and slopes are tracked.
> (7)
>
> (8)
>
> (9)
where,
Theandare the parameters to be determined with values from 0 to 1.
**Mean Square Error (MSE)**
Error measure is used to differentiate between a poor forecast model and a good forecast model. In other words, the error measure was used to find which model is the best. A model that has the smallest error is said to be the best model. MSE was chosen as an error measure because it is easy to understand and to calculate, and when used outside-sample usually matches the within-sample criterion.
> MSE = (10)
which
where,
is the actual observed value at time *t* and is the fitted value at time *t*.
**FINDINGS AND DISCUSSIONS**
# Data Description
The analysis has been done using the three techniques of exponential smoothing. First, the actual data of MYR against 1 USD is illustrated in Figure 1.
\[CHART\]
**Figure 1: The Actual Price of MYR**
Figure 1 shows the actual price of MYR starting from August 2013 to July 2018. It can be clearly seen that the price of MYR is increasing from 3.2865 in July 2013 to 4.065 in August 2018. The highest peak is in December 2016 with a value of 4.486 while the minimum value is in October 2013 with 3.1515. The graph contains a trend component but no identification of seasonal, irregular, and cyclical components exists. The trend line shows a positive slope exists indicating that for every one month increase, the MYR will increase about 0.0006.
**Single Exponential Smoothing**
\[CHART\]
**Figure 2: The Actual Price of MYR vs Single Exponential Smoothing Line of MYR**
Figure 2 shows the fitted and actual values of MYR using single exponential smoothing. The component exists is trend component and the two types of lines show a similar pattern. The MSE estimation is 0.01351 and MSE evaluation is 0.00404.
#
#
**Double Exponential Smoothing**
**Figure 3: The Actual Price of MYR vs Double Exponential Smoothing Line of MYR**
The fitted and actual values of MYR starting from September 2013 until Jun 2018 using double exponential smoothing is illustrated in Figure 3. The MSE estimation is 0.013521 and MSE evaluation is 0.004019. The MSE estimation of this method is slightly higher than using Single Exponential Smoothing and vice versa for MSE evaluation.
**Holt’s Method**
**Figure 4: The Actual Price of MYR vs Holt’s Method of MYR**
The similarity of the trend appears in Figure 4. which describes the fitted and actual values using Holt’s method. The MSE estimation is 2.95047 x 10-14 and MSE evaluation is 1.43915 x 10-14. The MSE evaluation for Holt’s is the lowest among the three methods.
Based on the analysis for the three exponential smoothing techniques above, the best model which is Holt’s method is used to predict the 12 steps ahead forecast value which is in August 2019. The forecast value is RM 4.30226 against 1 USD.
**CONCLUSION AND RECOMMENDATIONS**
As a conclusion, the first objective has been achieved as the best Exponential Smoothing Technique that describes MYR for 5 years period is Holt’s method. The comparison between the three Exponential Smoothing Techniques and the result showed that Holt’s method has the smallest value of error measure for both parts of data which are in the estimation and evaluation part. In order to forecast MYR 12 months ahead by using Holt’s method, the forecast value of MYR in August 2019 is RM 4.30226 over 1 USD. At the time the journal is written (19 July 2019), the MYR is RM 4.11. The up and down of the MYR is definitely rely on the political, economic, and psychological factors.
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