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Cover Letter

Cover Letter

Dear Sir/Ma’am,

I am Manas Tripathi, faculty at Indian Institute of Management (IIM) Rohtak, India. I along with my other co-authors Saurabh Kumar (Faculty at IIM Indore), and Sarveswar kumar Inani (Faculty at Jindal Global Business School) have worked on a novel problem of Exchange Rate Forecasting Using Ensemble Modeling for Better Policy Implications. The study have implications for policymakers, regulators, investors, speculators, and arbitrageurs.

We have used data of 7 years for three of the most traded currency pairs (EUR/USD, GBP/USD, and JPY/USD) and forecasted the next value using linear, non-linear, hybrid and ensemble methods. The highlights of the manuscript are given below:

1. An ensemble technique is proposed to forecast daily exchange rates for three currency pairs.

2. Ensemble combines three models: mean forecast, ARIMA, and artificial neural network.

3. Proposed methodology is able to forecast better as compared to individual models.

4. The study has implications for policymakers, regulators, investors, and speculators.

I am submitting the current manuscript for its possible publication in the prestigious Journal of Policy Modeling. I confirm that the manuscript is the original research article and has not been submitted elsewhere in any of the conferences or journals.

I hope the current manuscript aligns with the journal scope and objectives. Please let me know if anything else is required from my end.

Thanks and Regards

Manas Tripathi

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Title Page

Exchange Rate Forecasting Using Ensemble Modeling for Better Policy Implications

Manas Tripathia (Corresponding Author)a Faculty, Management Information Systems Area, Indian Institute of Management Rohtak, India

Email: [email protected]

Saurabh Kumarb

b Faculty, Information Systems Area, Indian Institute of Management Indore, India

Address: C-Block, Indian Institute of Management Indore, Indore, India- 453556

Phone No: +91-8542091617, Email: [email protected]

Sarveshwar Kumar Inanic

c Faculty, Finance Area, Jindal Global Business School, India

Email: [email protected]

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Anonymous Manuscript

Exchange Rate Forecasting Using Ensemble Modeling for Better Policy Implications

Abstract: This study aims to contribute in the area of foreign exchange forecasting. Exchange

rate plays an essential role for the economic policy of a country. Due to the floating exchange

rate regime, and ever-changing economic conditions, analysts have observed significant

volatility in the exchange rates. However, exchange rate forecasting has been a challenging task

before the analysts over the years. Various stakeholders such as the central bank, government,

and investors try to maximize the returns and minimize the risk in their decision-making using

exchange rate forecasting. The study aims to propose a novel ensemble technique to forecast

daily exchange rates for the three most traded currency pairs (EUR/USD, GBP/USD, and

JPY/USD). The ensemble technique combines the linear and non-linear time-series forecasting

techniques (mean forecast, ARIMA, and neural network) with their most optimal weights. We

have taken the data of more than seven years, and the results indicate that the proposed

methodology could be an effective technique to forecast better as compared to the component

models separately. The study has crucial economic and academic implications. The results

derived from this study would be useful for policymakers, regulators, investors, speculators, and

arbitrageurs.

Keywords: Neural Network, Currency Pairs, Forecasting, Ensemble, ARIMA Models, Exchange

Rate

JEL Classification: G15, G17, F31, C45

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1 Introduction

Foreign exchange rates are one of the very important factors in the international monetary

markets. It is widely known that exchange rates are affected by many micro-, macro-economic,

and political factors. This has motivated the researchers and practitioners to find the good

explanation for the movement of exchange rates (Ince & Trafalis, 2006; Qureshi, Rehman, &

Qureshi, 2018). Exchange rate forecasting has been an active area of research in computational

intelligence and econometrics. Exchange rate forecasting is an important constituent for the

economies especially in the context of leading economies as these economies are very sensitive

to external negative news. Researchers have proposed various econometric and time series

models to understand the volatility of exchange rates.

Time series forecasting has received significant attention across the world, in different

domains of management research, due to its applicability in different areas. One of the most

crucial areas in time series forecasting is modeling and forecasting a financial time series, such

as stock index, individual stocks, exchange-traded funds, exchange rates, etc. These financial

time series are affected by several economic and political conditions which include the stability

of the government, interest and inflation rates, national output, growth rate, employment, etc.

Therefore, it becomes imperative to identify an adequate model or underlying data generating

process, which can explain a financial time series. Time series forecasting is very useful

whenever there is very little information available about possible explanatory variables. Hence,

investors use technical analysis to forecast a financial time series. Technical analysis relies on

the assumption that historical patterns of a series could be used to forecast short-term and

medium-term forecasts of that series. In the long-run, technical analysis does not work well

because a financial time series depends on other economic, political, social, and psychological

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factors. In the literature, many studies have focused on the modeling and forecasting of a

financial time series (Adhikari & Agrawal, 2014; Buckley & O’Brien, 2017; Hussain, Knowles,

Lisboa, & El-Deredy, 2008; Prusa, Sagul, & Khoshgoftaar, 2018; Rodríguez-González, Colomo-

Palacios, Guldris-Iglesias, Gómez-Berbís, & García-Crespo, 2012).

There are various linear and non-linear methods in the literature to model and forecast a time

series. Among the linear models, Autoregressive Integrated Moving Average (ARIMA) (Box &

Jenkins, 1976) models have become a standard technique. The ARIMA model is discussed in

detail in the methodology section. ARIMA models without any autoregressive and moving

average term are called random walk model. Random walk models have found extensive use in

forecasting a financial time series, particularly exchange rates (Zhang, 2003). Though linear

models are simple and easy to use, the main problem is that they are not able to capture any

nonlinearity associated with the data (Dunis, Laws, & Schilling, 2012; Zhang, 2003).

Nonlinearity is an inherent characteristic of any financial time series because it gets affected by

many economic and social factors. Balkin and Ord (2000) suggest that artificial neural networks

(ANNs) are universal approximators and they are capable of identifying any nonlinear

relationships in the data. Therefore, ANNs could provide a promising solution to capture such

nonlinearities. The ANNs have found massive applications in the forecasting of economic and

financial time series (Alfaro, García, Gámez, & Elizondo, 2008; Choi, Yu, & Au, 2011; Huang,

Chen, Hsu, Chen, & Wu, 2004; Khansa & Liginlal, 2011; Lam, 2004; Lee & Yum, 1998; Pasley

& Austin, 2004; Panda & Narasimhan, 2007). ANNs have gained such popularity because of

their nonlinear, self-adaptive, data-driven, and non-parametric properties (Khashei & Bijari,

2010, 2011). Because of these salient characteristics, ANNs are proven to be better in forecasting

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financial time series having non-linearity. The extensive use of neural networks in various

business applications is shown in the systematic review by (Tkáč & Verner, 2016).

The studies comparing the performance of ARIMA and ANN models have yielded mixed

and inconsistent results (Zhang, Eddy Patuwo, & Y. Hu, 1998). Some studies have established

that ANNs forecast better as compared to ARIMA and random walk models (Dunis et al., 2012;

Ghazali, Jaafar Hussain, Mohd Nawi, & Mohamad, 2009; Sermpinis, Dunis, Laws, & Stasinakis,

2012). Whereas, some other studies have found that the forecasting accuracies of ANN are worse

than the simple random walk model for exchange rate forecasting (Hann & Steurer, 1996;

Taskaya-Temizel & Casey, 2005). Therefore, none of the methodologies is superior in all the

situations, and the blind use of any of them could provide inaccurate forecasting results. The

literature has confirmed that a financial time series contains both linear and non-linear patterns,

and hence, ANNs and ARIMA models could be used together to get better forecasting results

leading to better accuracy (Khashei & Bijari, 2011; Zhang, 2003). Therefore, we move towards

models, which combine random walk or ARIMA and ANN models. Such hybridization of

ARIMA and ANN was first proposed by Zhang (2003) and then popularized by some other

studies (Adhikari & Agrawal, 2014; Khashei & Bijari, 2010, 2011). The hybrid models are based

on the assumption that a financial time series contains linear and non-linear components, which

could be modelled separately from the series. In such models, first, the linear part is modelled by

the random walk or ARIMA models then the residuals of the model are computed. After

capturing the linear relationship, these residuals contain only nonlinear relationship. Then, ANN

models are used to model these residuals, and then the forecasts for the financial time series are

generated. The problem arises here because the forecasts of ARIMA and ANN models are

merely added, but their weights in the hybrid model are not considered to identify an optimal

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hybrid model. Therefore, we propose an ensemble model which calculate the optimum weights

for component models. These methods of combining models to form the ensemble are described

in detail in the methodology section.

We select exchange rate time series data because exchange rate forecasting has significant

implications for importers, exporters, investors, the central bank, and the government. We have

used the exchange rate data of the three most traded currency pairs (EUR/USD, GBP/USD, and

JPY/USD) to check the forecasting accuracy of our proposed ensemble model. We have taken

these currency pairs because these currencies belong to the most developed nations whose

economies impact the business of the entire world.

The motivation behind carrying out this study lies in the classical theories related to

international trade. The exchange rate fluctuation could impact international trade. The

contribution of the study is twofold. First, it proposes a novel ensemble technique to forecast

daily exchange rates for the three most traded currency pairs (EUR/USD, GBP/USD, and

JPY/USD). The ensemble technique combines the linear and non-linear time-series forecasting

techniques (mean forecast, ARIMA, and neural network) with their most optimal weights.

Second, the results of the study indicate that the proposed ensemble method could be an effective

technique to forecast better as compared to the component models separately. A hypothetical

case in the study also validates the predictive power of the ensemble model. The study has

crucial economic and academic implications. The results of the study would certainly be useful

for policymakers, regulators, investors, speculators, and arbitrageurs.

The paper consists of nine sections. Section 2 presents the theoretical foundation and

existing literature; Section 3 elaborates on the data collection; Section 4 illustrates the

methodology used in the study; Section 5 exhibits the empirical results; Section 6 discusses the

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results with a hypothetical case; Section 7 and Section 8 reveal the economic and academic

implications of the study; and finally, Section 9 concludes the study with limitations and the

future scope.

2 Theoretical Foundation

The motivation of this study lies in the heart of the theory of international trade, and theory

of trade and growth. Since exchange rate volatility and international trade are closely related, it is

pertinent to outline the theoretical background.

2.1 Theory of International Trade

The world has become a global market where countries exchange goods and services

amongst them. Countries differ in their productive capacity of goods and services, which forms

the basis for international trade. This difference in productive capacity causes differences in

prices, which are the main cause of international trade. International trade gives the opportunity

to every country to specialize in the production of those things in which they have a competitive

advantage. This results in the division of labor which enables the countries to focus on their

specialized skills and take advantage of the capabilities of other nations. Division of labor leads

to economies of scale which in turn leads to products with reduced cost and improved quality.

Authors have given different views on international trade. Adam Smith has described that

international trade takes place due to the absolute advantage countries have over other countries.

On the other hand, the Ricardian model suggests that the difference in technology and natural

resources are the basis for the countries to have a comparative advantage over other countries

(Dornbusch, Fischer, & Samuelson, 1977). The Ricardian model does not consider factor

endowment such as land, labor, and capital within a country. Alternatively, Heckscher–Ohlin

model (H–O model) proposes that differences in factor endowments are the basis for

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international trade between two countries (Heckscher & Ohlin, 1991). They further explain, that

a country exports those goods which are made by locally abundant resources in that country.

Similarly, a country will import those goods which require locally scarce resources.

The exchange rate is the price of one country’s currency with respect to the currency of

other country. Exchange rate, in principle, can affect international trade in many ways. Authors

have tried to understand the relationship between the volatility of the exchange rate and

international trade. Some authors have found that exchange rate volatility has an adverse effect

on international trade (Baron, 1976; Clark, 1973; Cushman, 1983). Péridy (2003) has found

mostly negative impact of exchange rate volatility on the export of G-7 countries. The study

further suggests that this impact of exchange rate volatility on exports is dependent on the

industries covered, and the destination market. Similarly, researchers have examined the impact

of exchange rate volatility on bilateral US trade using sectoral data (Byrne, Darby, &

MacDonald, 2008). They have found a significantly negative impact of exchange rate volatility

on US trade across sectors, strongest for exports of differentiated goods than that of homogenous

goods. However, authors have found a positive relationship between exchange rate volatility and

exports if the firms are able to reallocate their products to the domestic or foreign markets (Broll

& Eckwert, 1999). To deal with the fluctuations in exchange rates, firms use financial hedging

(Auboin & Ruta, 2012). In the view of the effect of exchange rate volatility on international

trade, it is essential to forecast the exchange rate in advance. This forms the core motivation of

our study.

2.2 Trade and Growth Theory

Trade implications of new growth theories are that trade and trade policies can influence

the long-run growth rate of the country. Trade and growth are interrelated to each other. There

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are three open economy versions of the canonical growth models, i.e., neoclassical growth

theory, learning-by-doing theory, and endogenous growth theory. Neoclassical growth model

focuses on factor accumulation. Learning-by-doing models emphasize accidental technological

progress. On the other hand, endogenous growth models center around motivated technological

progress. Trade enables the countries to import critical resources such as capital and intermediate

goods which have impact on long-run economic growth (Jayme Jr, 2001). These critical

resources are often quite expensive to produce locally. Authors have argued that openness to

trade, factor and technology flows, potentially contribute to the growth (Srinivasan & Bhagwati,

2001). Literature suggests that the exchange rate affects economic growth. Theory predicts that a

depreciating exchange rate boosts the exports of a country which will increase the gross domestic

product (GDP), but this holds mostly for developing countries (Rodrik, 2007). On the other hand,

developed countries are less likely to see benefits through the undervaluation of the exchange

rates. As the exchange rate has the significant impact of the economic growth of any country, it

is pertinent to study the forecasting of the exchange rates.

2.3 Financial Time Series Forecasting

The literature regarding forecasting financial time series is very vast. Hence, we would

present a brief review of the relevant literature which uses hybrid models. For linear data, ANNs

doesn’t perform better than ARIMA or random walk models. Because the data is having less

noise (disturbance), and we cannot expect ANNs to perform better than linear models for linear

relationships (Zhang et al., 1998). However, ARIMA and ANNs have gained success in their

linear and nonlinear domains, respectively. But none of them can be applied blindly for all

circumstances. It has become a standard practice to combine different models to overcome any

limitations posed by the component models and to improve the overall accuracy of the combined

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model. As it is very difficult to identify the linear and nonlinear characteristics of the data in the

real world, the combination of linear and nonlinear models could be a good strategy for practical

use (Khashei & Bijari, 2011). However, these hybrid models could not perform well in all the

circumstances (Taskaya-Temizel & Casey, 2005). In simple hybrid models, the first step is to

identify an ARIMA model to capture the linear structure of the data. In the second step, ANN is

trained on the residuals of the ARIMA model. Thus the future values are predicted by combining

both ANN and ARIMA.

Hybrid models could be homogeneous or heterogeneous. For example, if the hybrid model

is a combination of differently configured neural networks, it is termed as homogeneous.

Whereas, if both linear and nonlinear models are used to make a combination, it would be called

a heterogeneous hybrid model (Taskaya-Temizel & Casey, 2005). Both empirical, as well as

theoretical literature in the neural network forecasting, establish that the combining of different

methods or models could be an efficient way to improve the accuracy of the forecast

(Makridakis, 1989; Palm & Zellner, 1992). Various studies have used such hybrid models for

forecasting a time series (Luxhøj, Riis, & Stensballe, 1996; Wedding & Cios, 1996). In recent

years, several studies have used hybrid models which combine ARIMA and ANNs for modeling

and forecasting time series. Zhang (2003) uses hybrid models of ARIMA and ANNs on three

standard data sets, i.e., Wolf’s sunspot data, Canadian lynx data, and British pound/ US dollar

exchange rate data. The results reveal that the forecasting accuracy of hybrid models is better as

compared to that of either of the component models used separately. Khashei and Bijari (2010,

2011) propose a novel hybrid ARIMA-ANNs model, and the improved forecasting results are

obtained by such models for the same data sets used by Zhang (2003). Pai and Lin (2005)

combine ARIMA and support vector machines in forecasting stock prices problems, and finds

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promising results. Yu, Wang, and Lai (2005) propose a novel nonlinear ensemble forecasting

model integrating generalized linear auto-regression with ANNs to improve forecasting

performances in the foreign exchange market. Khashei, Reza Hejazi, and Bijari (2008) combine

ANNs with fuzzy regressions to forecast the financial market data, and the results show that such

models could be an effective alternate for forecasting a financial time series. Khashei, Bijari, and

Raissi Ardali (2009) integrate ARIMA models with ANNs and Fuzzy logic, and the findings

exhibit improved forecasting accuracy. Adhikari and Agrawal (2014) combine random walk

models with ANNs to four real-world financial time series, and the obtained results clearly show

that the hybrid model achieves better forecasting accuracies than individual component models.

Overall, it could be observed that the literature regarding forecasting the foreign exchange

rate is abundant. However, the studies employing hybrid models are very limited. This is one of

the first studies, to the best of our knowledge, which uses an ensemble model to forecast the

foreign exchange rate. The results of the study would be useful for policymakers, regulators,

investors, speculators, and arbitrageurs.

3 Data

The sample data in the current study consist of daily closing prices of three currency pairs –

Euro/US Dollar (EUR/USD), British Pound/ US Dollar (GBP/USD), and Japanese Yen/ US

Dollar (JPY/USD). The data has been obtained from the official website of the central banking

system of the United States which are certified by the Federal Reserve Bank of New York.1

1 Source: https://www.federalreserve.gov/releases/h10/hist/ [accessed on September 13, 2018]

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The sample period ranges from January 2009 to May 2016 (1848 observations). The data

before January 2009 is not considered deliberately to avoid the abnormal period of the subprime

crisis of 2008 which caused abnormal volatility in the market. Moreover, the inclusion of an

abnormal period could distort the results of the study. The returns for the currency pairs are

based on indirect exchange rate quotes of the foreign currencies (EUR, GBP, and JPY) with

respect to domestic currency (USD, and then logarithmic returns have been computed. The

logarithmic returns have been computed using equation (1) as follows:

Returnt=ln ( Pricet /Price t−1 )(1)

We divide the complete data into two subsets as the training and the testing datasets. The

period from January 2009 to March 2016 (1818 observations) is selected as the training set

which would be used to train the Neural Network model. The next 30 observations from the

months of April and May of 2016, which is not used in the training of the model, is set as the

testing set that would be used for checking the accuracy of the forecasting model.

The time series plots of all the three currency pairs are shown in Figure 1. The left side of

Figure 1 plots the prices of currencies at the level and the right side of the Figure plots the

logarithmic returns of that currency. It could be observed from Figure 1 that currency prices are

non-stationary, but their returns are stationary. To forecast a time-series, we need to ensure that

the time-series is stationary, i.e., the mean and the variance of the time-series are constant over

the sample period. We have employed Augmented Dickey-Fuller (ADF), and Phillips-Perron

(PP), unit root tests, to identify the stationarity properties of the exchange rates and returns. As

we are unaware of the true model for testing unit root, we would test two models: initially a

model with intercept only, and then a model with both intercept and trend. Optimal lag selection

for the ADF test is based upon Akaike information criterion (AIC). Currency exchange rates

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have been transformed into logarithmic values before applying the tests. The stationarity test

results have been reported in Table 1. We can reject the null hypothesis of non-stationarity, even

at 1% level of significance, for all three exchange rates after first differencing. Hence it could be

inferred that all three currency prices are non-stationary, but their returns are stationary.

<<Please insert Table 1 here>>

<<Please insert Figure 1 here>>

The descriptive statistics of the exchange rate returns are shown in Table 2. The mean daily

return is the lowest for EUR/USD, -0.011%. However, the volatility (standard deviation) is the

highest, 0.649%, for EUR/USD, which is very contradictory. Generally, the average mean has a

positive relationship with the volatility which can be observed in the other two currencies. The

mean daily returns for GBP/USD and JPY/USD are 0.000% and 0.010%, respectively with the

volatility of 0.599% and 0.647%, respectively. The skewness is negative for GBP/USD. Besides,

the kurtosis for GBP/USD pair is the highest (8.0951) among three pairs which suggest that the

GBP/USD pair has fat tails. The Jarque-Bera test statistic indicates that all three return series are

not distributed normally.


4 Framework and Methodology

The study proposes a NAM Ensemble Framework as shown in Figure 2, for forecasting the

time series data of currency pairs. NAM stands for Neural Network, ARIMA, and Mean

Forecast. NAM Ensemble Framework consists of four phases- data collection, data

transformation, application of analytical models on the data, and the results phase. The data

collection phase employs the collection of the three most widely traded currency pairs-

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EUR/USD, GBP/USD, and JPY/USD. The data transformation employs distributing the data

sample into training and testing data. The data transformation also employs the computation of

returns for each pair. After that, the analytical models of Neural Network, ARIMA, and Mean

Forecast are applied to the transformed data.


Ensemble model has been constructed by integrating the three analytical forecasting models

using linear optimization approach. ARIMA and Mean Forecast capture the linearity associated

with the data, and the techniques rely on the assumption that the future values are considered to

be the linear function of the past observations. But the financial time series data consist of both

linear and nonlinear patterns. Therefore, the Neural Network captures the non-linearity

associated with the data. In this section, the basic concepts of the three components of the

ensemble model –Mean Forecast, ARIMA, and ANN along with ensemble model are briefly

reviewed. We have used three different models and a hybrid ensemble model for predicting the

exchange rate returns for three currency exchange pairs, i.e., EUR/USD, GBP/USD and

JPY/USD.

4.1 Mean Forecast Model

The mean forecast model gives the forecast value as the sample mean of the historical data.

The model returns forecasts for an independent and identically distributed (iid) model which is

shown by equation (2) as given below:

Y t=µ+Z t (2)

Where Zt is a normal iid error. The forecasted value from the model is given by equation (3) as

shown below:

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Y n (h )=µ(3)

Where µ is estimated by the sample mean. Thus, the mean forecast model is the very basic

model forecasting the sample mean as the future values. The mean forecast model is used in

forecasting of time series data and can sometimes prove to be the best model for forecasting.

4.2 Autoregressive Integrated Moving Average (ARIMA) Model

The ARIMA models are most popular in modeling a time series due to its ease of

implementation. In an ARIMA (p, d, q) model, the future values are considered to be the linear

function of several past observations, i.e., autoregressive (AR) terms and random shocks, i.e.,

moving average (MA) terms (Box & Jenkins, 1976). In ARIMA (p, d, q), p stands for AR terms,

d stands for the number of differences required to make a series stationary, and q stands for MA

terms. ARIMA models could be pure AR models, pure MA models, the combination of the AR

and the MA, i.e., ARMA models. The ARIMA models could be used for stationary time series.

The stationary time series implies that the mean and variance is constant over time. The ARIMA

methodology tries to identify the true data-generating process based on the time series

observations. A step-by-step procedure for ARIMA modeling is provided in Box and Jenkins

(1976). If a time series is stationary, the number of the AR and MA terms could be identified by

correlograms (autocorrelation and partial autocorrelation functions). The ARIMA model is

shown in equation (4) and has the following form:

Y t=α +∑i=1

p

β iY t−i+∑j=1

q

γ j εt− j+εt (4 )

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Where α is the intercept term, Y is a time series, t is the point of time, and ε t is a white noise.

These ε t are independent and identically distributed (i.i.d.) normal variables, which has zero

mean and a constant variance. P and q are the number of AR and MA terms, respectively.

The Box and Jenkins (1976) methodology is a hit and error technique with three iterative

steps. The first step is model identification, the second is parameter estimation, and the third step

is diagnostic checking. The ARIMA model is identified from autocorrelation and partial

autocorrelation properties of the time series. Then, possible models are estimated, and the best

model is selected by some information criterion (such as Akaike information criterion). Before

identifying the model, it is necessary that the series under investigation is stationary. After

estimating the model, the adequacy of the model is tested by diagnostic tests. These tests are

basically to check whether the residuals of the model are i.i.d. This entire process is repeated

until a suitable model, satisfying the assumption about random errors, is found. The final

selected model can be used for the forecasting purpose.

4.3 Neural Network (NN) Model

Neural Network (NN) has the structure of the biological neural network and the learning

capabilities which can help in predicting future values based on past data. NN, as a machine

learning technique, is used in varied domains like credit ratings and approvals (Huang et al.,

2004), stock market prediction (Grudnitski & Osburn, 1993), debt risk assessment, and

bankruptcy prediction (Atiya, 2001; Kumar & Ravi, 2007; Wilson & Sharda, 1994). NN models

find its applications in both economic and financial time-series (Bildirici, Alp, & Ersin, 2010;

Bildirici & Ersin, 2009; Dunis et al., 2012; Özkan, 2013; Zhu, Wang, Xu, & Li, 2008).

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The NN model has an advantage over other models because it can capture the non-linearity

associated with the time series data of exchange rate returns. NN models have the function

mapping capability and are also referred to as universal approximators (Chen, Leung, & Daouk,

2003; Zhang & Qi, 2005). NN model can approximate a large number of inputs. The

configuration of neural network model consists of an input layer, hidden layers, and output layer

and the forecasting accuracy of NN model depends on both, number of inputs as well as the

configuration of NN model. The number of inputs determines the lag in the NN model. We have

used the feed-forward neural network in this study. The NN model used a back-propagation

learning method and is initially trained for forecasting only one-step ahead exchange rate. Multi-

step forecasts for exchange rate are then computed iteratively. The NN model is shown in

equation (5) and has the following form:

Y t=α 0+∑j=1

q

α j g (β0 j+∑i=1

p

β ij y t−i)+εt(5)

Where α j (j=0,1,2…,q) and β ij (i=0,1,2,…,p; j=1,2,..,q) are model parameters known as

connection weights; p and q are number of nodes in input and hidden layer; g is the transfer

function, which can be represented by equation (6).

g ( x )= 11+e−x (6)

The neural network model uses the exchange rates of a specific currency pair (EUR/USD,

GBP/USD and JPY/USD) as input nodes. The number of optimum lags is obtained as per the

AIC. The lag length for EUR/USD according to AIC comes out to be 2. Similarly, the lag length

of JPY/USD comes out to be 3, and for GBP/USD, the lag length comes out to be only 4. The lag

length in time series forecasting implies that a total of n nodes (equal to the lag length) would be

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used as inputs in the input layer of the feed-forward neural network. For instance, EUR/USD

based neural network has a lag length of 2 units, which implies that total two units would be used

as input to the neural network. Thus, the configuration of the neural network for EUR/USD

consists of 2-1-1 configuration. Hence, there would be overall three neural network models for

EUR/USD, GBP/USD, and JPY/USD currency pairs having the configurations of 2-1-1, 4-2-1

and 3-2-1 respectively. The generic neural network configuration of NN can be seen in Figure 3.


4.4 Ensemble Model

The ensemble model or hybrid model comprises of combining individual models to improve

the forecasting (Van Wezel & Potharst, 2007). Ensemble model produces better results than the

individual models whenever there is diversity in the dataset and the models (Coussement & De

Bock, 2013). Ensemble model has gained importance because of its wider applicability in

various domains (Bauer & Kohavi, 1999). The ensemble model gained its popularity in varied

domains primarily because of its simplicity to combine model with favourable performance and

yield better results. Ensemble model has been applied in both cross-sectional as well as time

series data. Similarly, the ensemble model has also been used in time series data for forecasting

purposes (Adhikari & Agrawal, 2014; Khashei & Bijari, 2011; Zhang, 2003).

Prediction of ensemble model in financial domain can be mainly grouped into two

categories: (i) segregating the linear and non-linear part in the time series data and then using one

forecasting model to capture the linear part and using other forecasting model to capture the

nonlinear part, then finally combining the two forecast model to yield the actual forecasted value

(Adhikari & Agrawal, 2014; Khashei & Bijari, 2011; Zhang, 2003); and (ii) the forecasted values

from each model are given weights to yield the final forecast value (Shmueli & Koppius, 2010).

19


The weights of each individual model could be given based on different methods like linear

optimization, analytical hierarchical processing, fuzzy sets, etc.

The current study employs the second type of ensemble models, where weights are obtained

by combining individual models through linear optimization. We have constructed an ensemble

of three models: ARIMA, Neural Network, and Mean Forecast. The weights (w1,w2, and w3) for

each of the three ensemble model (EUR/USD, GBP/USD and JPY/USD) were obtained by linear

optimization approach. The objective function in linear optimization approach is to minimize the

three error terms (RMSE, MAPE, and MAE) separately, keeping the constraint as the sum of

weights for each model should be unity. After that, the weights thus obtained are averaged across

the error terms to yield the final weight of each model in the ensemble.

5 Results

For comparing the efficiency of the neural network, we consider three widely used error

metrics – Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute

Percentage Error (MAPE) – as shown in Equation (7), (8) and (9) respectively.

RMSE=√∑i=1

n

(Y i−Y i )2

n (7)

MAE=∑i=1

n

|Y i−Y i|

n (8)

(9)

20


Where Y is the value of the time-series of the exchange rate returns. The lesser the value of

RMSE, MAE, and MAPE, the better is the accuracy of the model in forecasting the exchange

rate of the currency.

5.1 Ensemble for EUR/USD Currency Exchange Rate


The ensemble model for EUR/USD has a weightage of 33.33% for neural network model

and 66.67% for ARIMA model whereas Mean Forecast model has zero weightage in the

ensemble as shown in Figure 4. This implies that ARIMA has a higher weightage in the

composition of the ensemble model. The results for the EUR/USD currency exchange rate by

their error terms (RMSE, MAE, and MAPE) can be seen in Table 3.


We have taken six different horizons for the forecast (h=5, 10, 15, 20, 25 and 30). The last row

of each subpart in the table gives the average value of all forecasted horizons and ranking of a

particular model. The bold-faced values in each table indicate the best performing model. Thus,

an ensemble model with average RMSE value equal to 0.003750 seems to be the best performing

model for RMSE error metrics. The ensemble model closely competes with the neural network

model with RMSE value of 0.003753. Therefore, we can say that both neural network, as well as

the ensemble model, are able to forecast better for EUR/USD exchange rate in terms of RMSE.

For MAE, the bold-faced value of 0.00256 suggests that the Mean Forecast model is able to

predict better than all the other models. Mean Forecast model yield the average value of MAE as

0.00256, which is way better than the next competing models of ARIMA and Ensemble, having

21


the MAE of 0.00278. Thus, the Mean Forecast model is 8.59% better than its competing models

of ARIMA and Ensemble.

The results from Table 3 indicates that the ARIMA model is able to predict better than all

other models in terms of MAPE. The ARIMA model is considered better than other models

because the model yields the minimum value of MAPE, i.e., 104.6022, across all models. The

ARIMA model closely competes with the ensemble model, with MAPE value of 105.2602.

Therefore, we can say that both ARIMA, as well as Ensemble model, are able to forecast better

for EUR/USD exchange rate in terms of MAPE.

The models are ranked based on their error metrics. Thus, the ensemble model emerges as

the best model in terms of RMSE. Whereas the mean forecast model emerges as the best model

in terms of MAE, and ARIMA model emerges as the best model for MAPE. The overall average

rank obtained in Table 4 indicates that the ensemble model with an average ranking of 1.67

emerges as the best model for forecasting the returns of EUR/USD currency exchange rates.

5.2 Ensemble for GBP/USD Currency Exchange Rate


The ensemble model for GBP/USD has a weightage of just 11.33% for neural network and

88.67% for Mean Forecast model whereas ARIMA model does not have any significance in the

construction of ensemble model as shown in Figure 5.

The results of Table 4 indicates that the ensemble model is able to predict better than all

other models in terms of all the three error metrics, i.e., RMSE, MAE, and MAPE. The ensemble

model is considered best among all the models because the ensemble model yields the minimum

value of RMSE, MAE as well as MAPE. The ensemble model has the value of RMSE as

22


0.00618, MAE as 0.00508 and MAPE as 97.99. Therefore, we can say that the ensemble model

is able to forecast better for GBP/USD exchange rate.


Thus, the overall average rank obtained in Table 4 indicates that the ensemble model with an

average ranking of 1 emerges as the best model for forecasting the returns of the GBP/USD

currency exchange rates. This suggests that the performance of the ensemble model is more

robust and better than the individual models.

5.3 Ensemble for JPY/USD Currency Exchange Rate


The ensemble model for JPY/USD has a full weightage of 100% for neural network whereas

ARIMA and Mean Forecast model does not have any weightage in the ensemble as shown in

Figure 6. This can be attributed to the volatility of the exchange rate returns in the testing period.

The results of Table 5 indicates that the neural network model, the mean forecast model, and

the ensemble model are able to predict the JPY/USD currency exchange rate. The main reason

for having the same values of error metrics for both neural network model and the ensemble

model is that the neural network model has full 100% weightage in the ensemble model. The

neural network model and ensemble model yield the value of RMSE, MAE, and MAPE as

0.00801, 0.00619 and 104.6062 respectively.


The models are ranked based on their error metrics. Thus, the ensemble model along with

Neural network model and Mean Forecast model emerges as the best model, and the

23


performance of the ARIMA model is less than the performance of other three models. The

overall average rank obtained in Table 5 indicates that ensemble model, NN model and hybrid

model with an average ranking of 1.67 emerge as the best models for forecasting the returns of

JPY/USD currency exchange rates.

6 Discussion and Policy Implications

This study proposes a novel ensemble approach for exchange rate forecast. Ensemble

technique incorporates both linear and non-linear methods for exchange rate forecast. It assigns

weights to different linear and non-linear methods according to their prediction power. Ensemble

model comprises of different models to improve the forecasting power. We have used an

ensemble technique for exchange rate prediction for the three most traded currency pairs

(EUR/USD, GBP/USD, and JPY/USD). As it is evident from the hypothetical case, the exchange

rate forecasting is essential for the evaluation of risk and return associated with international

trade.

This study highlights that the performance of the ensemble model is more robust and better

than the individual models for all the three currency pairs, i.e., EUR/USD, GBP/USD, and

JPY/USD. In this study, we have formed an ensemble model using three different models, i.e.,

NN, ARIMA, and Mean Forecast model. Ensemble model gives a different set of weights to

these models for different currency pairs depending upon the predictive power of these models

for each currency pair. Moreover, the weight of NN in the ensemble model is highest (100%) for

the JPY-USD currency pair because the volatility of the JPY-USD pair is highest for the same

period. This confirms the fact that predictive power of NN is good for the volatile currency pair

(Inani, Tripathi, & Kumar, 2016). We have taken currency pairs of world’s largest economies

which will help investors and governments to evaluate the risk and return relationship of their

24


business decisions. Exchange rate forecasting is crucial in today’s economic scenario because

exchange rate volatility has a direct impact on international trade which in turn affects the world

economy.

A hypothetical case for the policy makers

Let us assume that an international trader has made a transaction worth USD 1 billion. Now,

we would show the economic benefits earned by employing the ensemble forecasting technique

vis-à-vis worst performing predictive model. The difference between the actual and predicted

price of the transaction would depend on the forecasting method we are using. We have

considered here the 30-days horizon (of the testing period of this study) for computing the

economic edge offered by employing an ensemble method. The forecasted prices from

forecasted returns have been computed by equation (10) derived from equation (1) as shown

below:

Returnt=ln ( Pricet /Price t−1 )(1)

Hence, Pricet / Pricet−1=antilog (Return¿¿ t )=eReturn t¿

Pricet=eR eturn t× Pricet−1(10)

Now, for computing the price at a particular time (t), we need to have both returns at the

time (t) and the price at the time (t-1). The actual price of EUR/USD on March 31, 2016, is 1.139

and the returns computed by the ARIMA model and ensemble model for April 1, 2016, are -

0.00032 and -0.00025 respectively. Thus, the price of EUR/USD on April 1, 2016, would be

1.13863 (=1.139*e−0.00032) for ARIMA model and 1.13871 (=1.139*e−0.00025). Likewise, we have

calculated the price for next 30-days. The details of the same can be seen in appendix 1.

25


After computing the forecasted prices, the MAE is computed. The computation of economic

benefit offered by the ensemble model is presented below step-wise for the EUR/USD currency

pair for 30-days testing period.

The value of transaction = USD 1 billion (as mentioned above)

Predicted value of EUR/USD by ARIMA = 0.005897158 euro/dollar

Predicted value of EUR/USD by Ensemble = 0.00584471 euro/dollar

Difference in predicted value by ensemble and ARIMA for USD 1 billion

= (0.005897158 - 0.00584471)* USD 1 billion = 52,448 euro = 0.052 Million euro

Similarly, we have calculated the economic benefit for other currency-pairs as shown in Table 6.


The economic edge of the ensemble is calculated by computing the difference between

predicted prices of the ensemble with respect to the worst performing predictive model. The

results of Table 6 suggest that the ensemble model improves the performance of the base model

by giving an economic edge of 0.052 million EUR, 3.13 million GBP, and 76.5 million JPY per

billion dollar transactions respectively. Along with traders, the ensemble model might give the

economic edge to arbitrageurs and speculators indulged in the foreign exchange market.

7 Economic Policy Implications

The behavior of the currency exchange market (FOREX) is irregular and random. The

reason behind that is exchange rates are dependent on many economic and political factors.

Hence, exchange rate prediction is not a simple task. The next obvious question arises “what is

the need to forecast the exchange rate?” This question has drawn the attention of researchers and

26


policymakers for many years. Investors and arbitrageurs follow exchange rate fluctuations and

get benefits from currency trading. Exchange rate prediction enables the policy makers to take an

appropriate decision about future investments. With the advent of floating exchange rate and

abandonment of the Bretton Woods System, the exchange rate is the principal channel through

which monetary policy affects the inflation and other economic activities. Floating exchange rate

mechanism is aimed to empower the policy makers to form the monetary policy independent of

external economic inequities. A better understanding of exchange rate movements is essential to

curb the inflation at a moderate level and keep the economic activities at a higher level.

Exchange rate reflects the financial and economic condition of the country. Hence,

understanding of the movement of the exchange rate will enable the policy makers to get timely

information about the financial and economic condition of the economy of a country.

Exchange rate prediction is an essential constituent of monetary policy of the national

economies especially in the context of leading market economies. These economies are very

sensitive to external negative news. Recently, Eurozone debt crisis, change in fuel prices, global

financial crisis, and tapering of US Federal Reserve’s quantitative easing have affected the

economic health of leading economies in the world. These negative news result in uncertainty in

economic world which in turn result in high volatility in the currencies of these countries. This

uncertainty in the movements of currency has led to the foundation of exchange rate prediction.

Exchange rate forecasting becomes important in the context of high-value economic transactions

in the form of debt and equity from multinational corporations and portfolio investors. This study

helps all the stakeholders such as central bank, government, and investors who are affected by

exchange rate volatility. The Central bank of a country intervenes in the forex market in case of

disruptive or undesirable movements in the exchange rates which may be unhealthy for the

27


internal and external sector of the economy (Kayal & Maheswaran, 2016; Prakash, 2012).

Central bank takes some quantitative as well as qualitative measures to ease down the volatility

of the currency. Hence, exchange rate prediction is essential for the central bank to bring the

desired economic stability in the country by ensuring currency behaving steadily without any

sharp moves.

The ensemble model incorporates both the linear as well as the nonlinear behavior of

exchange rate movements which may help the policy makers and economist to form a suitable

monetary policy for price stability and better economic activity. The finding further suggests that

the ensemble model better extracts the information hidden in the exchange rate which in turn

help the monetary authorities to have a better understanding of the financial and economic

condition of the economy. Better exchange rate prediction will help investors to form a profitable

trading strategy for currency trading.

8 Academic Implications

Researchers have been facing major challenges in devising an effective model for exchange

rate forecasting. Exchange rates often show irregular patterns which are difficult to predict for

researchers. This study proposes a new ensemble model which intelligently combines the three

models NN, ARIMA, and mean forecast model to forecast exchange rate. Empirical results

suggest that the ensemble model substantially improves the overall forecasting accuracies and

also outperforms each of the component models separately. This study contributes to the

literature of exchange rates prediction based on hybrid model. Earlier studies on hybrid model

mostly take equal weights for all the component models, but this study assigns the weights

according to the predictive power of the different component models present in the ensemble.

This finding can be an important implication for future researchers who want to predict the

28


exchange rate using some ensemble model. Moreover, this study highlights the fact that the

weight of NN in the ensemble model is highest for the most volatile currency pair, here

JPY/USD.

9 Conclusions, Limitations, and Future Research

The accuracy of exchange rate forecasting has been a crucial yet challenging task for

researchers in the past. Authors have used various time series models for exchange rate

prediction, yet research for effectiveness of forecasting models is still going. It has been

observed that combining predictive power from different models often leads to improved

performance. Hence, in this study, we have used an ensemble model comprising of three

different models, i.e., NN, ARIMA, and mean forecast model. In this study, we aim to forecast

the exchange rate for three currency pairs, i.e., EUR/USD, GBP/USD, and JPY/USD for the

period from January 2009 to May 2016. The results ascertain that the predictive power of

ensemble model is best for all the three currency pairs as compared to other models such as NN,

ARIMA, and mean forecast model. Moreover, when the exchange rate volatility is high, weight

for NN is coming to be highest in the ensemble model. This study contributes to the literature on

exchange rate prediction. Exchange rate prediction is imperative for various stakeholders such as

government, the central bank, and arbitrageurs to take their decision with minimum risk and

maximum returns.

We have taken only three currency pairs for exchange rate prediction. Future researchers can

try other combinations to examine the predictive power of the ensemble model. This will help

investors and government to take an appropriate financial decision in advance. We have used

ARIMA, NN and mean forecast models for this study; future researchers can use other

combination models in the ensemble. They can use other variants of NN such as Recurring NN

29


(RNN) and Higher Order NN (HONN) in the ensemble model. We have used data for the period

from January 2009 to May 2016 in our study. Future researchers may take the data before

January 2009 to observe the prediction power of the ensemble model in the period of the

subprime crisis of 2008 which caused abnormal volatility in the market.

Appendix 1

Calculation of price differences for EUR/USD (30-days testing period)

Date Actual Price

Returns(ARIMA)

Returns(ensemble)

Price(ARIMA)

Price(ensemble)

01-Apr-16 1.1385 -0.00032 -0.0002507 1.138637 1.13871504-Apr-16 1.1386 -9.6E-05 -9.216E-05 1.138528 1.1386105-Apr-16 1.1374 -5.9E-05 -6.786E-05 1.13846 1.13853206-Apr-16 1.143 -0.00014 -0.0001247 1.138295 1.1383907-Apr-16 1.1386 -0.00011 -0.0001009 1.138171 1.13827508-Apr-16 1.1406 -0.0001 -9.719E-05 1.138053 1.13816511-Apr-16 1.1412 -0.00012 -0.0001062 1.13792 1.13804412-Apr-16 1.1395 -0.00011 -0.0001024 1.137794 1.13792813-Apr-16 1.1281 -0.00011 -0.0001018 1.137668 1.13781214-Apr-16 1.1262 -0.00011 -0.0001032 1.13754 1.13769415-Apr-16 1.1295 -0.00011 -0.0001026 1.137413 1.13757718-Apr-16 1.1322 -0.00011 -0.0001025 1.137286 1.13746119-Apr-16 1.1375 -0.00011 -0.0001028 1.137159 1.13734420-Apr-16 1.133 -0.00011 -0.0001027 1.137032 1.13722721-Apr-16 1.1301 -0.00011 -0.0001027 1.136905 1.1371122-Apr-16 1.1239 -0.00011 -0.0001027 1.136778 1.13699425-Apr-16 1.1274 -0.00011 -0.0001027 1.136651 1.13687726-Apr-16 1.1318 -0.00011 -0.0001027 1.136524 1.1367627-Apr-16 1.1322 -0.00011 -0.0001027 1.136398 1.13664328-Apr-16 1.1325 -0.00011 -0.0001027 1.136271 1.13652729-Apr-16 1.1441 -0.00011 -0.0001027 1.136144 1.1364102-May-16 1.1516 -0.00011 -0.0001027 1.136017 1.13629303-May-16 1.1508 -0.00011 -0.0001027 1.13589 1.13617704-May-16 1.1486 -0.00011 -0.0001027 1.135763 1.1360605-May-16 1.1404 -0.00011 -0.0001027 1.135636 1.13594306-May-16 1.1421 -0.00011 -0.0001027 1.135509 1.13582709-May-16 1.1402 -0.00011 -0.0001027 1.135383 1.13571

30


10-May-16 1.1386 -0.00011 -0.0001027 1.135256 1.13559411-May-16 1.1444 -0.00011 -0.0001027 1.135129 1.13547712-May-16 1.138 -0.00011 -0.0001027 1.135002 1.13536

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Figures

1.0

1.1

1.2

1.3

1.4

1.5

1.6

09 10 11 12 13 14 15 16

EUR/USD

-.04

-.02

.00

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.06

09 10 11 12 13 14 15 16

Ret_EUR/USD

1.3

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1.6

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09 10 11 12 13 14 15 16

GBP/USD

-.06

-.04

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Ret_GBP/USD

70

80

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JPY/USD

-.06

-.04

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Ret_JPY/USD

Figure 1: Plots of prices and returns of the currencies. The left side of the Figure plots the

prices of currencies at the level, and the right side of the Figure plots the logarithmic

returns of that currency.

39

Figures

Figure 2: NAM Ensemble framework

Figure 3: Configuration of Neural Network model

40

Figures

Figure 4: Ensemble model for EUR/USD currency exchange rate

Figure 5: Ensemble model for the GBP/USD currency exchange rate

Figure 6: Ensemble model for JPY/USD currency exchange rate

41

Figures

42

Tables

Table 1. Stationarity test results

logarithm of EUR/USD logarithm of GBP/USD logarithm of JPY/USDModel and test Level FD Level FD Level FDWith intercept onlyADF -1.39 -43.29*** -2.91 -17.80*** -0.74 -31.72***PP -1.39 -43.31*** -2.83 -42.56*** -0.71 -43.02***With intercept and trendADF -2.26 -43.28*** -3.04 -17.83*** -1.57 -31.73***PP -2.23 -43.30*** -2.96 -42.58*** -1.55 -43.02***Notes: FD stands for first differences. *** indicates significance at 1% level of confidence. Only t-statistics

have been reported in this table to conserve space. The critical value for 1% level of significance is -3.43 for a

model with intercept only, whereas the critical value for a model with intercept and trend is -3.96 for 1%

level of significance.

Table 2. Descriptive statistics of daily exchange rate returns (January 2009 to May 2016)

EUR/USD GBP/USD JPY/USD Mean % -0.011 0.000 0.010 Median % 0.000 0.013 0.010 Maximum % 4.621 4.273 3.343 Minimum % -2.689 -4.966 -4.409 Standard Deviation % 0.649 0.599 0.647 Skewness 0.1842 -0.1652 0.0933 Kurtosis 5.3431 8.0951 6.7207

Jarque-Bera 432.9604 2006.213 1068.072 Probability 0.00 0.00 0.00 Observations 1847 1847 1847

Table 3. Model comparison for EUR/USD currency pairs

43

Tables

Error MetricsForecast Horizon

Neural Network ARIMA Mean

Forecast Ensemble

RMSE h=5 0.00284 0.00285 0.00383 0.00284h=10 0.00384 0.00384 0.00384 0.00384h=15 0.00371 0.00371 0.00383 0.00371h=20 0.00362 0.00362 0.00383 0.00362h=25 0.00431 0.00431 0.00383 0.00431h=30 0.0042 0.0042 0.00383 0.0042

Average 0.003753 0.00376 0.00383 0.00375Rank 2 3 4 1

MAE h=5 0.00204 0.00202 0.00256 0.00202h=10 0.00256 0.00256 0.00256 0.00255h=15 0.00281 0.0028 0.00256 0.00281h=20 0.00278 0.00277 0.00256 0.00278h=25 0.00328 0.00327 0.00256 0.00328h=30 0.00324 0.00323 0.00256 0.00323

Average 0.002785 0.00278 0.00256 0.00278Rank 3 2 1 2

MAPE h=5 112.3334 106.233 110.264 108.267h=10 107.1046 104.407 110.264 105.306h=15 104.9239 103.185 110.264 103.765h=20 106.6567 106.298 110.264 106.418h=25 104.6988 104.212 110.264 104.374h=30 103.7399 103.278 110.264 103.432

Average 106.5762167 104.6022 110.2641 105.2602Rank 3 1 4 2

Average Rank 2.67 2 3 1.67

Table 4. Model comparison for GBP/USD currency pairs

44

Tables



Forecast Ensemble

RMSE h=5 0.00799 0.00781 0.00648 0.00768h=10 0.00718 0.00687 0.00648 0.00652h=15 0.0066 0.00622 0.00648 0.00604h=20 0.00638 0.00592 0.00648 0.0059h=25 0.00606 0.00582 0.00648 0.00568h=30 0.00563 0.00543 0.00648 0.00528

Average 0.00664 0.00635 0.00648 0.00618Rank 4 2 3 1

MAE h=5 0.00766 0.00684 0.00515 0.00658h=10 0.00598 0.00558 0.00515 0.00515h=15 0.00546 0.00492 0.00515 0.00486h=20 0.00538 0.00484 0.00515 0.00488h=25 0.00511 0.00478 0.00515 0.00469h=30 0.00465 0.00441 0.00515 0.00432

Average 0.00571 0.00523 0.00515 0.00508Rank 4 3 2 1

MAPE h=5 186.672 93.456 100.229 87.6349h=10 195.671 137.262 100.229 99.9037h=15 162.704 114.257 100.229 99.798h=20 148.524 111.564 100.229 100.037h=25 141.489 109.427 100.229 100.364h=30 134.069 108.4 100.229 100.239

Average 161.5213 112.3942 100.2289 97.99607Rank 4 3 2 1

Average Rank 4 2.67 2.33 1

Table 5. Model comparison for JPY/USD currency pairs

45

Tables



Forecast Ensemble

RMSE h=5 0.00907 0.00913 0.00709 0.00907h=10 0.00709 0.00712 0.00709 0.00709h=15 0.00599 0.00602 0.00709 0.00599h=20 0.00872 0.00874 0.00709 0.00872h=25 0.00856 0.00857 0.00709 0.00856h=30 0.00863 0.00864 0.00709 0.00863

Average 0.00801 0.00804 0.00709 0.00801Rank 2 3 1 2

MAE h=5 0.00815 0.00826 0.00595 0.00815h=10 0.00595 0.006 0.00595 0.00595h=15 0.00474 0.00478 0.00595 0.00474h=20 0.006 0.00602 0.00595 0.006h=25 0.00599 0.00601 0.00595 0.00599h=30 0.00629 0.00631 0.00595 0.00629

Average 0.00619 0.00623 0.00595 0.00619Rank 2 3 1 2

MAPE h=5 101.572 104.116 113.129 101.572h=10 110.984 113.915 113.129 110.984h=15 106.981 108.878 113.129 106.981h=20 103.209 104.278 113.129 103.209h=25 102.724 103.607 113.129 102.724h=30 102.168 102.885 113.129 102.168

Average 104.6062 106.2796 113.1294 104.6062Rank 1 2 3 1

Average Rank 1.67 2.67 1.67 1.67

Table 6. Calculation of economic edge

46

Tables

Worst Performing model

Ensemble Economic Edge (Ensemble vs. worst model)

Predicted EUR/USD 5897157.93(ARIMA) 5844710.08

52,448 EUR =0.052 million EUR (approx.)

Predicted GBP/USD

17760292.5 (NN) 14627348 3132944 GBP =3.13 million GBP (approx.)

Predicted JPY/USD

3687812442(ARIMA) 3611318464 76493979 JPY = 76.5 million JPY (approx.)

Assumption: Transaction of USD 1 billion

47

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