A Forecasting Model for KWD/EURO Exchange Rate
Bedour Alsaleh1*
1 Department of Industrial & Management Systems Engineering, College of Engineering & Petroleum, Kuwait University
*Corresponding Author: bedour.alsaleh@ku.edu.kw Accepted: 15 August 2021 | Published: 1 September 2021
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Abstract: The current study was carried out to build a statistical model for forecasting the KWD/EURO exchange rate. Statistical analysis for the exponential smoothing models was performed. The accuracy measures criteria, such as mean absolute error (MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE), stationary R-Squared, and R-Squared were assessed. The results of the analysis reveal that the Winters’ Additive model was the best model among the exponential models that were investigated. Data collection was carried out over six months daily; from 1st of January 2021 till 26th of June 2021.
Keywords: Exchange rates, Exponential smoothing, KWD, EURO
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1. Introduction
CBK's policy for the Kuwaiti Dinar (KWD) exchange rate aims at enhancing the relative stability of the KWD against other currencies especially the US Dollar and shields the domestic economy against the effects of imported inflation. This reflects the importance of the exchange rate policy in the Kuwaiti economy where there are no restrictions on the movement of funds.
From 18 March 1975 until 2002, the CBK followed an exchange rate policy of pegging the KWD to a weighted currency basket. That policy based the determination of the KWD exchange rate on a special weighted basket of currencies of the countries that have significant trade and financial relations with the State of Kuwait. It had proved its effectiveness in achieving a high degree of relative stability in the KWD exchange rate against major world currencies.
From 5 January 2003 to 19 May 2007, the KWD was pegged to the US Dollar, according to the Decree No. 266/2002 that stipulates pegging the KWD exchange rate to the US Dollar within margins around a parity rate as of the beginning of the year 2003. H.E. Sheikh Salem Abdulaziz Al-Sabah, the Governor, announced the parity rate of the KWD exchange rate against the US Dollar for the first day of business in January 2003 corresponding to Sunday 5 January 2003. This rate was set at 299.63 fils per dollar with margins of ±3.5%. Therefore, the KWD exchange rate against the US Dollar after the 5th of January 2003 was neither to exceed 310.11 fils/dollar nor to fall below 289.14 fils/dollar. This parity rate was set using the same principles and considerations employed historically by CBK to determine the KWD exchange rate under the previous system of the currency basket to ensure a smooth change from the currency basket peg to the dollar peg within margins. However, the period since 2003 witnessed persistent decline in the US dollar exchange rates against major currencies; therefore, putting upward pressures on the KWD exchange rate against the US dollar.
Starting from 20 May 2007 the KWD exchange rate against the USD is pegged to an undisclosed weighted basket of international currencies of Kuwait’s major trade and financial partner countries, by virtue of the Decree No. 147/2007, thus reverting back to the exchange rate policy followed prior to 2003. In a statement to the press, H.E. Sheikh Salem Abdulaziz Al-Sabah, the Governor, indicated that the move aims at protecting the purchasing power of the national currency and containing inflationary pressures in the local economy, after having exhausted all attempts to absorb the adverse effects of USD depreciation against major currencies for an extended period of time.
To determine exchange rate movements of the Kuwaiti Dinar (KWD) and other currencies, forecasters conduct in-depth research on a variety of economic indicators and other factors. To provide accurate forecasts, six factors are used to determine averages needed to make predictions. These include equity flow, short-term interest rate differentials, long-term interest rate differentials, trade and current account balances, relative growth, and inflation differentials. Additionally, forecasters rank various economic indicators and factors that they believed to be of significance, which is how movement of exchange rates is determined.
Most people know that a variety of influences affect foreign exchange rates, which are based on economic factors. Each of these factors is unique to the country, some being more important than others are. Because of this, experts responsible for determining foreign exchange rate forecasts must compare and then rank all the sensitivities and degrees of these sensitivities so a determination can be made as to the currencies that respond and the currencies that do not respond.
The process of foreign exchange rate forecasting is relatively complicated but extremely valuable for understanding the history, as well as short and long-term increases and decreases for every currency in the world.
The foreign exchange market has grown remarkably in the last few decades. The major factors that have contributed to the phenomenal growth of currency markets are the introduction of floating exchange rates and the swift development of global trading markets. Foreign exchange markets and exchange rates have been characterized by dramatic changes over time, as a result of market crashes or rallies, changes in economic policy, and business cycles. Such changes make the exchange rate unpredictable, volatile, noisy, non-stationary, and chaotic. However, exchange rates play a critical role in determining the success of many businesses and financial institutions around the globe. Thus, the accurate prediction of the exchange rate will largely benefit multinational firms and financial institutions.
However, predicting the direction of the movement of exchange rates of the Kuwaiti dinar (KWD) is interesting in itself given the fact that the KWD was pegged to a basket of currencies for more than 28 years. This kind of exchange rate policy is much different from one using a floating currency or one pegged to a single currency. Under this exchange rate arrangement, the KWD showed notable movements against most major currencies. In addition, studying the KWD exchange rate movements is more interesting when one knows that the Central Bank of Kuwait never declared what currencies the basket contains or what the weights of these currencies are.
The exchange rate reflects the ratio at which one currency can be exchanged with another currency, namely the ratio of currency prices. The question that arises is related to the behavior in the short term of the exchange rates, and how these fluctuations might affect the financial
market players, the investors as well as those directly influenced by changes in the exchange rate. To forecast exchange rates there are numerous models, which are complicated for modeling the relationship between currencies, but those interested do not always have the resources needed to fully benefit from them, or as suggested by the literature, most exchange rate models based on macroeconomic data are considered outperformed. So, prediction methods based on the random walk models and exponential smoothing techniques can be used in capturing the fluctuations in the short run. The main objective of this study is to present the performance of methods for the task of exchange rate forecasting, using the exchange rates of KWD versus EURO.
2. Literature Review
Exchange rate is the most important elements of monetary transmission process and movement in this price that has a significant pass-through to consumer price. There is a link between language and currency. Language is a medium of communication and currency is a medium of exchange. National, ethnic, and liturgical languages are here to stay, but a common world language, understood as a second language everywhere, would obviously facilitate international understanding. By the same token, national or regional currencies will be with us for a long time in the next centuries, but a common world currency, understood as the second most important currency in every country, in which values could be communicated and payments made everywhere, would be a magnificent step toward increased prosperity and improved international organization.
International transactions are usually settled in the near future. Exchange rate forecasts are necessary to evaluate the foreign denominated cash flows involved in international transactions. Thus, exchange rate forecasting is very important to evaluate the benefits and risks attached to the international business environment. Many academics and practitioners suggest several approaches to forecast exchange rate like; demand supply (balance of payment) approach, monetary approach, asset approach, portfolio balance approach, uncovered interest parity models and forward rate approach. Empirical studies use some of them very frequently especially monetary approach in different versions like flexible price monetary model (Frankel 1976, Bilson 1978), the sticky price monetary model (Dornbusch 1976, Frankel 1979b) and Hooper–Morton model (Meese & Rogoff 1983, Alexander & Thomas 1987, Schinasi & Swami 1989, and Meese & Rose 1991).
Meese and Rogoff (1983) compared a number of time series and structural models on the basis of out of sample forecasting accuracy and found that in the short horizon (less than one year) random walk model outperforms a range of fundamentals based models of exchange rate determination, but the same author (Meese and Rogoff, 1983b) in another study found that the random walk models do not yield the minimum forecast errors when forecast horizon is extended to periods beyond one year. In the long run, structural models perform more accurately than random models. Although the Meese–Rogoff’s findings were remarkably robust, several authors found models whose out of sample forecasting performance improves upon a random walk (MacDonald and Taylor, 1993; Chinn and Meese, 1995; Mark, 1995;
MacDonald and Marsh, 1997). In recent time, some researchers (Van Dijk 1998, Kilian 1999 and Berkowitz and Giorgianni 2001) even questioned the inference procedures and robustness of results of these studies and argued that although difficult but still possible to beat random walk models. Hogan (1985) compared different structural and time series models; PPP model, forward exchange theory, sticky price monetary models. Forward rates give superior forecasts at a horizon of one quarter. At the two-quarter forecasting horizon, uncovered interest parity is
the preferred model. While for the remaining horizon dynamic specification of the sticky price monetary model outperformed all other models, including random walk models. Franklin (1981) and Boothe and Glassman (1987) found that monetary/asset models are not very useful to explain the movements in exchange rates under flexible exchange rate system. John Faust et al (2002) examined the real-time forecasting performance of standard exchange rate models.
A recent development in the focus came by the work of some of the researchers like (Balke &
Fomby 1997; Taylor & Peel 2000; Taylor et al. 2001). They argued that underlying economic theories are fundamentally sound, still economic exchange rate models were not able to give superior forecasting performance because these models assume a linear relationship between the data. In reality these data show nonlinearity. They argued that underlying fundamentals shows long run equilibrium condition only, towards which the economy adjust in a nonlinear fashion (Mahesh, 2005). In this this study, Statistical analysis for the exponential smoothing models was performed and produces superior result.
3. Methodology
The major advantage of exponential smoothing methods is that they are simple, intuitive, and easily understood. These methods are quite useful for routine short-term forecasting of large numbers of time series such as currencies exchange rate prices. Exponential smoothing is regarded as an inexpensive technique that gives forecasts that are "good enough" in a wide variety of applications. For these applications building a more sophisticated model (or learning enough to understand a more complex model) would not be worth the required time and money.
Moreover, the repetitive nature of the calculations means that exponential smoothing methods can be programmed quite easily into a digital computer. In fact, it is quite easy to do this using a personal computer and some of the widely available spreadsheet languages (such as LOTUS 1-2-3). In addition, data storage requirements are minimal. Often the use of more sophisticated forecasting models requires expensive computer packages and access to a mainframe computer.
A major disadvantage of exponential smoothing is that no formal model-building methodology exists. The choice of an exponential smoothing method will often depend on the interpretation of a plot of the time series. The choice of a particular technique will require that the practitioner decide whether a trend exists. If a trend exists, some kinds of trend must be postulated. The practitioner must also decide whether seasonal variation exists. If seasonal variation does exist, the kind of seasonal variation—increasing or constant (that is, multiplicative or additive)—
must be arrived at. As we have seen, the different exponential smoothing techniques have been designed to handle different scenarios. Method selection is largely a matter of matching the data plot with an appropriate scenario. Trying several methods and comparing them based on the sum of squared one-period-ahead forecast errors when the methods are applied to a historical data set is often a useful strategy. When this is done, the value of the smoothing constant should be determined objectively by using the historical data set for each smoothing method tried (note that the best smoothing constant for one method may not be the best for other techniques). It is common to choose a particular method based on the experience a practitioner has had with other, successful applications of exponential smoothing.
Four techniques of exponential smoothing have been employed; they are:
A Single Exponential Smoothing (SES).
Suppose that the time series y1, …. yn is described by the model yt = βo + ε t.
Where the average level βo may be slowly changing over time. Then the estimate ɑ0 (T) of βo
made in time period T is given by the smoothing equation ɑ0 (T) = αyT + (1- α)ɑ0 (T-1).
Where α is smoothing constant between 0 and 1 and ɑ0 (T-1) is the estimate of βo made in time period T - 1.
A point forecast made in time period T for yT+τ is ŷT+τ = ɑ0 (T). Where is a time horizon. This model is applied assuming that the series is stationary, without trend. Simple exponential smoothing is used for short–range forecasting. The value of α is usually determined by minimizing the sum of squares of the forecast errors.
Holt-Winters' Two-Parameter Double Exponential Smoothing (HDES) Suppose that the time series y1, …. yn described by the model.
yt = βo + β1 t + ε t.
Where the parameters β0 and β1 may be slowly changing over time.
Two-parameter double exponential smoothing is a smoothing approach for forecasting such a time series that employs two smoothing constants.
Suppose that in time period T-1 we have an estimate ɑ0 (T-1) of the average level of the time series That is, ɑ0 (T-1) is an estimate of the intercept of the time series when the time origin is considered to be time period T-1. Also suppose that in time period T-1 we have an estimate b1(T-1) of the slope parameter β1. If we observe yT in time period T, then we can update ɑ0 (T- 1) and b1(T-1) then we can compute point estimate follows:
If we observe yT in time period 'T, then
1. We obtain an updated estimate ɑ0 (T) of the intercept parameter β0 by using the equation ɑ0 (T) = αyT + (1- α)[ɑ0 (T-1) + b1(T-1)]
where α is a smoothing constant between 0 and 1.
2. We obtain an updated estimate b1(T) of the slope parameter β1 by using the equation b1(T) = β[ ɑ0 (T) - ɑ0 (T-1)] + (1- β) b1(T-1)
where βis a smoothing constant between 0 and 1.
3. A point forecast of the future value yT+τ made at time T is ŷT+τ(T) = ɑ0 (T) + b1(T)τ
This model is appropriate for series with linear trend and no seasonal variations.
Holt-Winters' Multiplicative Exponential Smoothing (HMES)
Winters' method is an exponential smoothing approach to handling seasonal data. Although the method is not based on a formal statistical model, multiplicative Winters' method is generally considered to be best suited to forecasting a time series that can be described by the equation.
yt = (βo + β1 t) × SNt + εt.
Where the time series parameters may be slowly changing over time.
The intercept is β0 and the slope is β1 and SNt is the multiplicative seasonal factor.
Each of these three coefficients are defined by the following recursions:
ɑ0 (T)=α
( ) ( ) ( + 1 − ) ( − 1 ) ( +
1− 1 )
= − a T b T
L T sn T y
a
t T
+(1-α ) [ ɑ0 (T -1)+ b1(T-1)].
Where α is a smoothing constant between 0 and 1.
b1(T) = β[ ɑ0 (T) - ɑ0 (T-1)] + (1- β) b1(T-1).
Where β is a smoothing constant between 0 and 1.
Snt (T)=
( ) ( ) ( )
sn(
T L)
T a T y
snt =
t + 1−
T − +(1- γ) SnT (T-L) where γ is a smoothing constant between 0 and 1.
The initial estimate of the trend component, β1 is:
( ) ( )
m L y b ym0 1 1
1 −
= −
The initial estimate of the intercept component, β0 is:
( ) ( )
0 0 1 2Lb1y a = −
The initial estimate of the multiplicative seasonal factor, Snt (0) =s
( ) for t L
n s n L s
sn L
t t t
t 0 1,,,,,,,,,
1
=
=
= for t =1,..L Holt-Winters' Additive Exponential Smoothing (HAES)
Additive Winters' method is a modification for handling a time series that displays constant seasonal variation. The method is generally regarded as best suited to forecasting time series that can be described by the equation:
yt =( βo + β1t) +SNt + εt
Where SNt is the additive seasonal factor, the intercept is βo and the slope is β1.
The model parameters may be slowly changing over time. Each of these three coefficients are defined by the following recursions:
ɑ0 (T)=α[yT – SnT (T-L)]+(1- α)[ɑ0 (T -1) b1 (T-1)], where α is a smoothing constant between 0 and 1.
b1(T)= β[ ɑ0 (T) - ɑ0 (T-1)]+(1- β) b1(T-1), where β is a smoothing constant between 0 and 1.
snt (T)= γ [yT - ɑ0 (T)] +(1 - γ) snT (T-L), where γ is a smoothing constant between 0 and 1.
4. Data Description
Data of KWD Dinar exchange rate against EURO have carried out over six months daily; from 1st of January 2021 till 26th of June 2021.
5. Stationary Estimation
The first step in any time series analysis is to inspect the plot of the series, from figure 1 it is obvious that the series does not exhibit upward and downward trend. A series seems to be stationary, also the series has a seasonal pattern with some major peaks and several minor peaks.
Figure 1: Actual values of Euro with respect to 1 KWD in a daily basis.
Figure 2: Graph of Euro over time (1st Difference form)
Figure 2 shows the result of first order differencing. The figure illustrate that the first order differencing has gone a long way to inducing stationary.
Fitting of simple exponential smoothing, winter's Additive exponential smoothing, and winter's multiplicative exponential smoothing.
Simple Exponential Smoothing (SES)
Table 1: Results of the Simple Exponential Smoothing
Model fit statistics for seasonal simple exponential model with RMSE and MAE smallest errors and R-squared is high.
Table 2: Exponential Smoothing Model Parameters
It is clear from table 2 that = 0.943 is the best smoothing parameter with standard error SE= 0.076 and t-test is significant.
Winter's Additive Exponential Smoothing (WAES)
Table 3: Results of the Winters Additive
It is clear from table-3 RMSE=0.009 and MAE=0.006 are smallest with α= 0.917, γ = 2.51x10-7 and δ =1.55x10-5 Exponential smoothing parameters.
Exponential smoothing parameters are shown in table 4.
Table 4: Exponential Smoothing Model Parameters
It is clear from table 4 that the value of α= 0.917 is the best smoothing parameter with standard error SE= 0.076 and t-test is significant.
Winter's Multiplicative Exponential Smoothing (WMES)
Table 5: Results of the multiplicative exponential smoothing with model fit statistics
It is clear from table 5 that the RMSE=0.009 and MAE=0.006 are the smallest fit statistics with exponential smoothing parameters α= 0.921, γ = 0.001 and δ = 0.357.
Smoothing parameters for the multiplicative exponential smoothing model are shown in table 6.
Table 6: Exponential Smoothing Model Parameters
Residual Model Diagnostics
Residual model diagnostics have been conducted with respect to the following: -
● Normality.
● Constant variance.
● Independence
To check the validity of the assumptions plot of residuals was created for normality, constant variance, and independence assumptions. Plots are in appendices for all models.
The normal plot of the residuals have a straight- line appearance approximately, which indicate that a normality assumptions hold, the pattern in which the residuals fluctuate around the zero indicate the constant variance assumption hold , due to the fact that the residual plot form a horizontal band appearance and finally a plot of residuals against fit values suggest that, there is no positive or negative autocorrelation exits in error terms, which indicates that the error terms occur in a random pattern over time. Therefore, these error terms are statistically independent.
Forecasting Results
The forecasting results are measured by the following indicators:
● Mean absolute error (MAE).
● Mean absolute percentage error (MAPE).
● Root mean square error (RMSE).
These measures are used to compare the forecasting accuracy of the various models. The rule of thumb is the smaller of MAE, RMSE and MAPE the better is the forecasting ability. The model with the smallest of the accuracy measures will be the best to be used for forecasting.
7. Comparison of Models
Table7 Accuracy Indicators
Measures Simple Exponential Winters’ Additive Winters’ Multiplicative
RMSE 0.009 0.009 0.009
MAPE 0.227 0.225 0.234
MAE 0.006 0.006 0.006
Stationary R-Squared 0.446 0.451 0.419
R-Squared 0.924 0.925 0.921
An important objective of this study is to search the best predictive performance model among all the competitive models, table-7 shows the summary results for all three seasonal models, the best model is the Winters' Additive model. The performance predictability of the candidate model is illustrated in Figure 3.
Figure 3 shows the forecast performance of Winters' Additive model as the line of fit values is close to the line of the actual values.
Figure 3: Winter’s Additive Model
Out-of-Sample Forecasting
Out -of- sample forecasting conducted using the candidate model Winters' Additive model, to study the behavior of the EURO prices during the future period started from 4th day of the 26th week for the year 2021 till the 7th day of the 30th week. Figure 4 illustrates the sharply downward trend of the EURO price with seasonal pattern.
Figure 4: Forecasting Euro Prices
Figure 4 shows that the behavior of EURO price is decline over the next three years. The model used to forecast out sample observations is holt-winters' multiplicative model.
Table 8: EURO forecasting prices.
Date. Format: "WWWW DDD" Predicted value from X3-Model_1
1 26 SUN 2.6851
2 26 MON 2.7070
3 26 TUE 2.7075
4 26 WED 2.6907
5 26 THU 2.6734
6 26 FRI 2.6751
7 26 SAT 2.6766
8 27 SUN 2.6771
9 27 MON 2.6770
10 27 TUE 2.6754
11 27 WED 2.6730
12 27 THU 2.6717
13 27 FRI 2.6734
14 27 SAT 2.6749
15 28 SUN 2.6754
16 28 MON 2.6753
17 28 TUE 2.6737
18 28 WED 2.6713
19 28 THU 2.6700
20 28 FRI 2.6717
21 28 SAT 2.6732
22 29 SUN 2.6737
23 29 MON 2.6736
24 29 TUE 2.6720
25 29 WED 2.6696
26 29 THU 2.6683
27 29 FRI 2.6700
28 29 SAT 2.6715
29 30 SUN 2.6720
30 30 MON 2.6719
31 30 TUE 2.6703
32 30 WED 2.6679
33 30 THU 2.6666
34 30 FRI 2.6683
35 30 SAT 2.6698
8. Conclusion
This study assessed the predictive capabilities of the KWD/EURO exchange rate forecasting models. Results show that the Winters' Additive model was superior compared to the simple exponential and the Winter's multiplicative exponential smoothing models that were investigated. The candidate model is used to study the behavior of the EURO prices during the future period started from 4th day of the 26th week for the year 2021 till the 7th day of the 30th week. The forecasted trend of the EURO price was sharply downward with seasonal pattern.
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