Forecasting Exchange Rate

Forecasting Exchange Rates

 

  • Abstract:
The work of this thesis primarily revolves around the concept of forecasting the daily exchange rates of the European Euro valued in United States Dollars. Forecasting is a relatively important issue in business operations, however it is also one of the most problematic. With the uncertainty of the future, forecasts are difficult to assess. The aim of this thesis is to successfully forecast the future exchange rates of the European Euro in terms of United States Dollars for the month of May 2010, and determine whether the forecasting models properly work when applied to exchange rates, why or why not, and their measure of accuracy. The methodology of this thesis revolves extensively around quantitative research, largely including a probability and forecasting approach.
 
Throughout a period of three months, actual exchange rate values were collected and recorded to form a data set. The exchange rate data was then used in the application of a variety of mathematical forecasting models to forecast the daily exchange rates for a
future, one-month period. Upon measuring the accuracy of the forecasts, the forecasted exchange rates contained very little error. Therefore, the forecasts are considered to be successful, and the hypothesis that exchange rates could be determined with the aid of a mathematical forecasting model is accepted. Though it is very difficult to consistently estimate exchange rates successfully, the work of this thesis shows there is always a greater probability of benefiting from a forecast.
 

                               INTRODUCTION

1.1 Description and Motivation for Topic

The work of this thesis primarily revolves around the concept of forecasting the daily exchange rates of the European Euro (EUR) valued in United States Dollars (USD).
 
Throughout a period of three months, actual exchange rate values were collected and recorded to form a data set. The exchange rate data was then used in the application of a variety of forecasting models to forecast the daily exchange rates for a future, one month period. As the month approached, the actual exchange rates were collected and recorded. Lastly, the actual exchange rates were compared with the forecasted exchange rates to form an analysis that measured the forecasting accuracy of the various models.
 
The thesis has been largely motivated by an operations management course and a statistics course completed by the author. With a curiosity to perform a forecast upon completion of the operations management course, the thesis topic was developed
instantaneously.

1.2 Aim of Research

Forecasting is a relatively important issue in business operations, however it also happens to be one of the most problematic of issues. Because the future is always uncertain, forecasts are difficult to assess; yet they are rarely ever avoidable in effective business planning. The aim of this thesis is to successfully forecast the future exchange rates of the EUR in terms of USD for the month of May 2010.
Furthermore, the author expects to determine whether the forecasting models properly work when applied to exchange rates, why or why not, and their measures of accuracy.

1.3 Hypotheses

  •  Future exchange rates can be determined with the aid of a mathematical forecasting model.
  •  Future exchange rates cannot be determined with the aid of a mathematical forecasting model.
 

1.4 Description of Methods

The methodology of this thesis revolves extensively around quantitative research, and largely includes a probability and forecasting approach. The forecasting system that is implemented involves the determining of an appropriate sample size, a collection of the necessary data, the application of relevant forecasting models, and an analysis of the results. Additionally, a variety of mathematical models that are commonly used in forecasting are applied to the sample of collected exchange rate data. These models include a naive approach, a moving average, exponential smoothing, and linear regression.

1.5 Limitations

It is evident that forecasting exchange rates is no simple task. Therefore, a variety of limitations are present within the work of this thesis. Foremost, there are approximately one hundred eighty-two currencies in existence throughout the world.
 
The foreign exchange rate data that is used in this thesis only includes two currencies, which happen to be one of the most common pairs in currency trading. Due to the lack of randomness, a biased selection of variables exist; making it unknown whether or not the same results would be achieved when using a different, unbiased, pair of currencies. Furthermore, there are numerous forecasting models available, however, this thesis only includes models that are familiar to the author. Therefore, it is uncertain whether these models are actually efficient in forecasting exchange rates.
 
Additionally, it is imperative to bear in mind that the forecasting models used in this thesis do not support the probability of natural disasters or political/economical factors occurring. Lastly, since exchange rates do not typically follow an identifiable trend, it is difficult to conclude whether or not the same results would be achieved at a different period of time.

1.6 Technical frame of reference

A majority of the theories that this thesis is based upon have been referenced from four significant works of literature. Lind, Marchal, and Mason’s “Statistical Techniques in Business & Economics” (2002) was a fundamental element in interpreting the theories of correlation, linear regression, indexes, and dispersion.
 
Mendenhall, Reinmuth, and Beaver’s “Statistics for Management and Economics” (1993) was essential in supporting the theories of the measures of central tendency, as well as the measures of forecast accuracy. Heizer and Render’s “Operations Management” (2004) was the core foundation for explaining the theory of forecasting. Lastly, Henderson’s “Currency Strategy” (2002) and Rosenberg’s “Exchange-Rate Determination” (2003) provided the framework for the context of exchange rates. Additional text was referenced from relevant internet sites that contained theories pertaining to forecasting and exchange rates.
 
 
 
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TABLE OF CONTENTS
 

1 INTRODUCTION……………………………………………….

1.1 Description and Motivation for Topic …………….
1.2 Aim of Research ………………………………………………..
1.3 Hypotheses…………………………………………………………..
1.4 Description of Methods…………………………………………….
1.5 Limitations ………………………………………………………………….
1.6 Technical frame of reference…………………………………………..

2 DESCRIPTIVE MEASURES ……………………………….

2.1 Numerical Descriptive Methods…………………………………………..
2.2 Measures of Central Tendency ………………………………..
2.2.1 Mean………………………………
2.2.2 Median ………………………………………..
2.2.3 Mode……………………………
2.3 Measures of Variability …………………………….
2.3.1 Range …………………………………..
2.3.2 Variance……………….
2.3.3 Standard Deviation …………………………..
2.4 Simple Index Numbers ……………………………….
2.5 Example Calculations of Numerical Descriptive Methods ……..
2.5.1 Data ………………..
2.5.2 Mean………………
2.5.3 Median ………………………………………..
2.5.4 Mode………………
2.5.5 Range ……………
2.5.6 Population Variance………………………………………………….
2.5.9 Population Standard Deviation ………………………………………
2.5.8 Sample Variance……………………………………………………..
2.5.10 Sample Standard Deviation ……………………………………
2.5.8 Simple Index Numbers……………………………..

3 BACKGROUND OF FORECASTING…………………..

3.1 Forecasting Approaches…………………………………………..
3.1.1 Quantitative Forecasting…………..
3.1.2 Econometric Forecasting 
3.1.3 Time-series Forecasting Models………………………………………………………..
3.2.1 Types of Forecasts ……………………………………………
3.2.2 Time Horizons………………………………………………………….
3.3 Forecasting System…………………………………………………
3.4 Importance of Forecasting………………………………………………..

4 FORECASTING MODELS

4.1 Naive Approach …………………………………………………..
4.2 Simple Moving Averages…………………………………………….
4.3 Exponential Smoothing………………………………………………..
4.3.1 Smoothing Constant ………………………………………..
4.4 Exponential Smoothing with Trend Adjustment…………..
4.5 Linear Regression 
4.6.1 Assumptions Underlying Linear Regression…………………………………….
4.6.2 The Standard Error of Estimate …………………………………..
4.6.3 Correlation Analysis ……………………..

5 MEASURING ERROR……………………….

5.1 Measures of Forecast Accuracy ………………………………………
5.2 Mean Absolute Deviation…………………………………………
5.3 Mean Squared Error ……………………………………………..
5.4 Root Mean Square Error ………………………………………….
5.5 Mean Absolute Percentage Error ……………………………………

6 EXCHANGE RATES……………………………………………

6.1 Background of Foreign Exchange Rates………………………………………. 
6.2 Forecasting Exchange Rates …………………………………………..
6.2.1 Influencing Factors………………………………………..
6.2.2 Economical Forecasting Models ……………………………………………….
6.2.3 Time Horizons………………………………………………….
6.3 Limitations ………………………………….

7  DATA

8 CALCULATIONS FOR FORECASTING THE EXCHANGERATES 

8.1 Naive Approach …………………………………………………..
8.2 Moving Average…………………………………..
8.3 Exponential Smoothing………………………………………………………
8.4 Exponential Smoothing With Trend Adjustment …………
8.5 Linear Regression ……………………………………………..
9 CALCULATIONS FOR MEASURING ERROR…………
9.1 Mean Absolute Deviation………………..
9.2 Mean Squared Error ………………………………..
9.3 Root Mean Squared Error ……………………………………
9.4 Mean Absolute Percentage Error ………………………….
10 RESULTS……………………………………………………………
11 CONCLUSION ………………………………………………………………
 
 

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