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1 Student: Bo Palmgren MSc Finance and International Business Student Id: Academic Advisor: Frédèric Warzynski Department of Economics Utilizing a technical and fundamental analysis to develop a framework for forecasting electricity prices in Denmark, Finland, Norway, and Sweden Aarhus School of Business, Aarhus University Summer 2008

2 Author s Declaration I hereby declare that I am the sole author of this thesis. I authorize Aarhus School of Business, Aarhus University to lend or to reproduce this thesis by photocopying, in total or in part, to other institutions or individuals for the purpose of scholarly research. Bo Palmgren MSc Finance and International Business Aarhus, August 1 st 2008 I further declare that the data from Nord Pool is only used for scholarly research and is printed in summary versions as in accordance with agreements made with Nord Pool. Bo Palmgren MSc Finance and International Business Aarhus, August 1 st

3 Abstract: The extreme volatility experienced by electricity prices, means that accurate forecasting is a critical concern for market participants either for developing bidding strategies or for making production decisions. Many methodologies have been applied in forecasting electricity prices, but the view of the author is that more accurate forecasting can be developed by exploring and merging the methodologies of the technical analysis and the fundamental analysis. Accordingly the research firstly creates a forecast framework based upon a technical analysis, where spot prices are forecasted using an ARMA and GARCH (1, 1) approach. Secondly a forecast framework is created based upon a fundamental analysis, where the research explore the relationship between electricity price and factors such as, temperature, wind, rain, reservoir level, and marginal costs. Thirdly the technical and fundamental analysis is merged. Computed test results demonstrates that for the selected forecast periods the technical forecast models produces an average Mean Absolute Percentage Error of 3.37 percentage, which is superior to the average of the fundamental forecast models 6.75 percent. The combinations of the technical and fundamental forecast models are however most effective with an average Mean Absolute Percentage Error of 2.10 percent. The results however are complicated when used as a tool for risk management. The reason being, that due to the measurement frequency the technical models are able to provide estimated values for each hour of the day, whereas the fundamental models and the merged models are able to provide an average daily estimate. Keywords: Forecast, ARMA, GARCH (1, 1), Technical Analysis, Fundamental Analysis, Electricity Prices, Nord Pool, and Elspot. 3

4 Acknowledgements This project would not have been possible or so successful without the valuable contributions and help from the following people: Frédèric Warzynski, my advisor. Thank you for allowing me to explore. Cagdas Ozan Ates, Head of Intraday Trading at Dansk Commodities A/S. Thank you for introducing the topic to me. Kasper Thor Sørensen, Client Training Executive at Thomson Reuters. Thank you for allowing me access to your 3000 Xtra database. Pontus Ripstrand, Market Data Services at Nord Pool. Thank you for allowing me access to your FTP server. To fellow students, you know who you are. Thank you for discussion, commenting and editing remarks. 4

5 Table of Contents 1. INTRODUCTION THEORETICAL BACKGROUND THE NORDIC ELECTRICITY MARKET THE NORDIC GENERATION OF ELECTRICITY AND ITS COSTS THE RESEARCH PROBLEM STATEMENT OF PROBLEM DELIMITATION LITERATURE REVIEW FINANCE AND FORECAST LITERATURE ELECTRICITY PRICE-BEHAVIOR LITERATURE FORECAST METHODOLOGY AND METHOD FORECAST METHODOLOGY FORECAST METHODS FORECAST FRAMEWORK NORD POOL Market Participants Elspot THE TECHNICAL ANALYSIS Data Evaluation and Presentation Analysis THE FUNDAMENTAL ANALYSIS Data Evaluation and Presentation Analysis APPLICATION OF THE FORECAST FRAMEWORK TECHNICAL FORECAST MODELS Models Presentation Models Forecast FUNDAMENTAL FORECAST MODELS Models Presentation Models Forecast THE MERGED MODELS Models Presentation Models Forecast MODELS COMPARISONS A RISK MANAGEMENT PERSPECTIVE CONCLUSION SHORTCOMINGS AND SUGGESTIONS FOR FURTHER RESEARCH BIBLIOGRAPHY

6 APPENDIX A APPENDIX B APPENDIX C APPENDIX D APPENDIX E APPENDIX F APPENDIX G APPENDIX H APPENDIX I APPENDIX J APPENDIX K APPENDIX L APPENDIX M APPENDIX N APPENDIX O APPENDIX P APPENDIX Q APPENDIX R APPENDIX S APPENDIX T APPENDIX U APPENDIX V APPENDIX W APPENDIX Y

7 1. Introduction On the 20 December 2007 at 6.00 pm in West Denmark the market price per MWh of electricity was 4027 NOK. Five days later at 6.00 pm the price was 163 NOK per MWh. The importance of forecasting electricity prices comes from its extreme volatility. The above example demonstrates the vast amount of money that can be lost without proper insight. Historically the electricity market of each Nordic country has been a monopoly controlled by the Government. However starting with Norway in 1992, each Nordic country has deregulated its electricity market and introduced competitive forces. Nord Pool is the Nordic power exchange, which operates the competitive marketplace for the Nordic electricity market. Nord Pool provides market places for trading physical and financial contracts. The physical market comprises the market known as Elspot. Elspot is the common Nordic market for trading physical electricity contracts with next-day supply, also known as the day-ahead market. The aim of the research is to guide the reader through an in-depth analysis of the trends and influential factors affecting electricity prices on the Elspot market. This should provide the foundation for the creation of several reliable and justifiable models to forecast prices on the Elspot market. The formulation of such models will be useful for understanding price behavior and for formulating appropriate strategies for risk management. Accordingly a generator (producer) of electricity will benefit from having an estimate of the future price as it will enable him to formulate an appropriate production schedule in accordance with his marginal cost. A retailer and a commodity trader will benefit from the estimate of the future price to develop a profitable strategy for where and when to either buy or sell electricity within the Nordic region. What separates this research from the other researches is how it separates and exploits the data in accordance with trends detected and the focus on several influential fundamental 7

8 factors, where the research tries to specify and quantify a relationship with electricity prices. The research is organized as follows: Part two introduces the Nordic electricity market by briefly discussing its history, value chain and its generation methods and costs. Part three introduces the research problem and part four reviews relevant literature within finance and electricity price-behavior in relation to the identified problem. Part five explains the methodology and methods taken by the research. In part six the forecast framework introduces Nord Pool by briefly discussing its market participants and the Elspot market. Part six further contains a technical and fundamental analysis on the spot price. In part seven the research presents empirical evidence on the forecasting abilities of the research approach. Lastly parts eight and nine reflect and conclude on the research process with special focus on the application of the research within the context of risk management. 8

9 2. Theoretical Background The theoretical background gives a general description of the Nordic electricity market. The theoretical background part will firstly describe the electricity market with special focus on the markets historical development and its value chain. Secondly, the theoretical background will describe the various means Nordic countries have in generating electricity and the associated cost of each generation method. The aim is that the theoretical background will serve as the foundation of the research by ensuring that the reader obtains fundamental knowledge for understanding later parts and becomes acquainted with terminology used. 2.1 The Nordic Electricity Market In 1879 Thomas Edison was focused on developing an electrical system that could provide people with a practical source of energy to power his new invented light bulbs. In his pursue he developed the first electric power plant that was able to generate electricity and carry it to people s home. The power plant called Edison s Pearl Street Power Station began its generation of direct current (DC) electricity on September 4, 1882, in New York City. About 85 customers in lower Manhattan received enough electricity to light 5000 lamps. DC electricity however was impractical for sending electricity over long distances. Thus turning point of the electricity market came when William Stanley, Jr. invented a transformer that enabled transmitting alternating current (AC). AC electricity enabled power plants to transport electricity much further than before. Consequently in 1885, George Washington opened the first major power plant at Niagara Falls using AC electricity. In comparison the Niagara Falls power plant could transport electricity more than 300 kilometers, whereas the Edison s Peal Street Power Station could transport electricity within two square kilometers In the Nordic countries DC electricity was dominant until the Second World War. This meant the Nordic electricity market was characterized by many small local power plants often owned by local municipalities. However the emergence of AC electricity combined with the requirement of guaranteeing universal access to the electrical grid meant that 9

10 gradually the small local power plants stated merging into large governmentally controlled firms, hence monopolies were created 1. The formation of a monopolized Nordic electricity market was also due to various unique characteristics. For instance, as total generating capacity available must exceed the demand to handle peak periods there is a need for electric utility to maintain sizeable reserves above the normal load to ensure reliability 2. As electric utility facilities furthermore are very expensive and require many years to secure permits and construct the generally accepted view was, that the public interest was best served by electric utilities being operated as monopolies. In the late 1970s Chile was the first country to introduce competitive forces into the electricity market. This gradually led other countries to consider the possibility of a deregulated electricity market 3. The general approach taken in developing a competitive electricity market was to divide the value chain as illustrated in figure 2.1 and allow the generations and retailing to be competitive, while the transmission was kept under Government control. This approach was also taken for the competitive Nordic electricity market. Figure 2.1 The Value Chain of the Electricity Market Energy Source Generation Transmission Distribution End-Users 1 Appendix A provides a historical time line for electricity. 2 Appendix B provides an overview of the Nordic electricity demand. 3 For differences in the national electricity markets see Wolak,

11 The reason for desiring a deregulated electricity market had its theoretical foundation in an increased economic surplus as illustrated in figure The triangle B, C, and D represent the deadweight loss under a monopoly, which disappears with a competitive market. Consequently a competitive market increases the economic surplus for the society through a decrease in the price and an increase in the quantity. For later parts it is worth noticing that different marginal costs leads to different prices as in accordance with figure 2.2. Figure 2.2 The Electricity Market from a Microeconomic Perspective P r i c e A Pm F B Monopoly Price Area Ppc E D C Perfect Competition Price/MC MR AR Quantity Note: MR = Marginal Revenue and AR = Aggregated Revenue = Demand. In figure 2.2 it is illustrated that a competitive market is desirable. However since the deregulation vast amount of literature has been published claiming that there is still market power in the electricity market (e.g. Hylleberg, 2004, Wolfram, 1999, or Wolak, 2003). The existence of market power within the Nordic electricity market means that an area for the price is formed between a monopoly and perfect competition. Consequently the 4 Economic surplus is the consumer surplus added with the producer surplus. Consumer surplus is the amount the consumers benefits from by being able to buy the product for a price less than what they are willing to pay. Producer surplus is the amount that the producer benefits from being able to sell the product for a price higher than they would be willing to sell it for. 11

12 presence of market power is likely to cause higher and perhaps even more volatile prices, than the fundamentals suggest. This causes a natural concern for the research as such behavior is irrational and not easily modeled. The existence of market power within the electricity market has lead to academic discussion of the objectives and the optimal market design of a Nordic electricity market. Nord Pool claims that there are three main objectives of a deregulated electricity market 5. To obtain a better balance between power generation capacity and power demand To increase efficiency within the power industry To reduce regional differences in the electricity prices to end-users Whether these three objectives are obtained from the current market structure that Nord Pool is practicing is a debated issue. Particular so, as there are limits on the capacity for the transmission grid. This works against the achievement of reducing regional differences, which is to say that the efficiency and balance between generation and demand is reduced. 2.2 The Nordic Generation of Electricity and its Costs Electricity generation is the process of converting some form of energy into electricity. Electricity is measured in watts, where one watt is the power equal to one joule of energy per second and describes the rate at which electricity is being used at a specific moment. Watts uses a measurement terminology to reflect larger amounts as illustrated below. 1 Kilowatt (KWh) = 1000 Watts 1 Megawatt (MWh) = Watts 1 Gigawatt (GWh) = Watts 1 Terawatt (TWh) = Watts 5 As identified by Nord Pool in their report The Nordic Power Market - Electricity Power Exchange across National Borders 12

13 In most parts of the world electricity is generated by electro-mechanical generators, primary driven by heat engines fuelled by coal, gas, nuclear fusion 6, or oil normally referred to as thermal power. Other generation methods such as kinetic energy of flowing water, also known as hydro power, and wind are significant alternatives and highly relevant when discussing the Nordic countries. In general it is possible to divide the Nordic countries generation of electricity into four categories as illustrated in figure Figure 2.3 The Nordic Electricity Generation Methods Hydro Power Hydro power is the force of energy created by moving water. To generate hydro power a certain geographical location is needed, where massive water flows are present or can be created. Such a geographical location is present in Northern Scandinavia, where the rain and snow flows down the mountains and in to the dams, which generates hydro power. An advantage of hydro power is its ability to handle seasonal and daily fluctuation in consumption of electricity. When consumptions increases or decreases the dam simply releases or stores its water supplies. Dams have a maximum capacity and if it is reached 6 Although nuclear fusion technically belongs to the thermal power group the research will treat it separately. 7 Appendix C provides a more technical description of each electricity generation method. 13

14 water is released and thereby an oversupply of electricity happens, which causes prices to fall drastically. Wind Power Wind electricity power is produce by windmills that use large spinning blades to capture the kinetic energy in moving wind, which then is transferred to rotors that produce power. This electricity is transmitted through wiring down the tower and into the transmission grid. Nuclear Power Condensing power plants fuelled by uranium are called nuclear power plants. Nuclear energy is produced by a controlled nuclear chain reaction. This creates heat and is used to boil water, which produces steam, and drives a steam turbine. The turbine generates electricity. Thus compared with hydro power nuclear power is based on science and can be done anywhere. Thermal Condensing Thermal power stations produce electricity by heating water, which turns into steam. To heat the water the power plant uses fossil fuels such as coal, gas, and oil (uranium considered above). Thus as nuclear power it is scientifically created and therefore can be created anywhere. Often thermal power plants utilizes the steam it produces to also produce heat, therefore thermal generation can also be referred to as combined heat and power generation (the differences will be highlighted). Compared to hydro power it should be noticed that thermal power stations use fuel commodities, which often comes at a considerable cost. From a historical perspective oil was the main fuel used until the oil crisis; however since the oil crisis plants using coal and gas have become dominant 8. Table 2.1 illustrates the amount of electricity generated in 2006 for each Nordic country in accordance with each generation method. 8 For a historical development of the Nordic electricity generation sources please refer to Appendix D. 14

15 Table 2.1 Nordic Generation of Electricity in GWh 2006 Denmark Norway Finland Sweden All Share of total (%) Total generation % Nuclear power % Thermal power % - Condensing Power Combined Heat and Power Hydro power % Wind power % Source: Nordel Annually Statistic Firstly, observe that approximately half of the Nordic electricity generation is from hydro power. Secondly observe that nuclear power and thermal power roughly generates 25 percent of the total Nordic generation respectively. Further examination of each country in relation to its generation method reveals that the Norwegian generation is almost purely from hydro power. Denmark generates its electricity from combined heat and power plants, but also has a considerable amount of wind generation, which in 2006 amounted to nearly 15 percent of the total Danish electricity generation. Finland uses a variety of electricity generation methods. The largest source of electricity generation is thermal condensing with nearly 60 percent but note, that unlike Denmark both thermal condensing power and combined heat and power is generated. The remaining Finish electricity generations comes from nuclear power and hydro power, which generates 28 and 15 percent respectively. Sweden also uses a variety of generation methods. The most dominant source of electricity is nuclear power, which generated 46 percent. This is followed by hydro power which generated 44 percent and thermal condensing which generate roughly 9 percent 9. The marginal cost of the above identified generation methods are different and is unfortunately an industry secret. Nord Pool however has provided an indication of each generation methods costs. The illustration below will serve as a reference point for the difference in the marginal costs of generating electricity. 9 Percentage for each generation method for each Nordic country is calculated in accordance with the numbers presented in table

16 Figure 2.4 Estimates for the various Production Cost of Electricity Source: From Nord Pool s report The Nordic Power Market - Electricity Power Exchange across National Borders Figure 2.4 sums up that hydro power is the cheapest option, followed by wind power, nuclear power, combined power and heating, and finally the condensing methods. This means the Norwegian electricity generators have the lowest marginal cost. The Swedish and Finish generators, both have low cost from hydro and nuclear power generation, but also depend on more expensive thermal condensing methods. The Danish generators have low cost from wind power and high costs from combined power and heat generation. Note that the low cost of hydro power means that surpluses of electricity in the Northern region of hydro power should be transmitted to Southern regions. In relation to the discussion of the objective of the Nordic electricity market this means that adequate grid transmission capacity must be available to carry this North-to-South flow in order to reduce regional price differences. 3. The Research Problem Given above introduction and theoretical background a general understanding of the Nordic electricity market should have been obtained and it now seems appropriate to discuss the problems of the research. As stated the overall aim of the research is to forecast Nordic electricity prices and for that reason an understanding of Nord Pool and the Elspot market is necessary. 16

17 When forecasting it is important to recognize that forecasts are just that, forecasts, and often little more than a second best guess. Thus while any forecast is a guess, the conclusions are based upon deriving the right theoretical framework for proclaiming, which factors are justifiable in explaining electricity prices. Accordingly in order to answer the research problems a foundation should be found in economic theory and sound reasoning for justifying, which factors influence the price of electricity in Nordic countries. The self evident criteria for the forecast is accuracy and for obvious decision-making reasons a narrow band of uncertainty is preferred to wider bands of uncertainty. As any research the results will only obtain a true meaning, if it is applicable. Accordingly the last part of the research will elaborate on how the research results could provide a foundation for risk management. 3.1 Statement of Problem To ensure that the research reaches an objective and an applicable outcome this section identifies the research problems. The main problem of the research is as follows: Is it possible to create fitting forecast models of electricity prices quoted on the Elspot market of Nord Pool? Several sub-problems has furthered been formulated, which will assist in answering the main problem of the paper. The sub-problems are divided so it follows the natural flow of the research, which will be further explained in the methodology section. Consequently in order to avoid ambiguity the sub-problems are as follows: Nord Pool - What characterizes Nord Pool and the Elspot market? - How does Nord Pool organize its trade at Elspot? - Do any of the characteristics of the Elspot market lead to a specific forecast approach? 17

18 Technical Analysis - Do electricity prices exhibit seasonality? - Are electricity prices mean-reverting? - Do electricity prices have any trends that could be exploited for forecasting? Fundamental Analysis - Which factors influence the electricity prices in the Nordic countries? - Is it possible to quantify these factors into components that are theoretically sound and have an influence on the price of electricity? Applicability - Can strategies for risk managements be developed based upon the developed forecast models? 3.2 Delimitation The electricity transmission grid and new derivatives offer by Nord Pool provides the possibilities to speculate between other electricity markets in Europe and in the future market. The research however delimits itself from looking into these opportunities and will stay focus on the Nordic region and the Elspot market. These delimitations are critical as at least Germany is believed to be influential on electricity prices in the Nordic region due its grid connection with Denmark and Sweden. The point tariff system which is the fixed amount paid for pouring and tapping electricity is not considered decisive for the research and therefore it is not considered. The same goes for taxes, which will also be considered a non-decisive factor for the results achieved. The Norwegian electricity market is complicated and depending on grid congestion it can be divided into several price areas. The research however delimits itself to only examine the Norwegian markets as divided into North and South. This is how the Norwegian market is structured for the majority of the time and therefore no major difference in the results and its applicability is expected. 18

19 As discussed in the theoretical background insufficient grid capacity is an obstacle for a uniform price for the whole Nordic region. The research however, will delimit itself from investigating grid capacities thoroughly. The reason for doing so is that it is considered worthy of a thesis in itself, as forecasting methods would have to be developed along with collection of appropriated data. Break-downs for electricity generators have the possibility of affecting the price greatly as a shortage might arise. However estimating production stop also does not seem possible and therefore it is not considered. Similarly as explained in the theoretical background overflow in the dams can lead to a considerably drop in the price. Such behavior however is not considered in the research as it would seem impossible without any proper insight information to model such behavior. 4. Literature Review The literature review will provide the foundation for the research approaches and methods. 4.1 Finance and Forecast Literature The forecasting theory used in the research has its origin in the Box-Jenkins methodology (Box and Jenkins, 1976) and the fundamental analysis (Graham and Dodd, 1934). The Box-Jenkins methodology applies autoregressive moving average models (ARMA or ARIMA) to find the best fit of a time series to forecast an exogenous variable. The fundamental analysis claims that markets may misprice a security in the short run but the correct price will eventually be reached. Hence profits can be made by trading the mispriced security and then waiting for the market to recognize its mistake and re-price the security Associated closely with the Box-Jenkins methodology and the fundamental analysis is the efficient market hypothesis (EMH) (Fama, 1970). The interpretation of the EMH is divided into three efficiency hypothesis. The first hypothesis states that excess return cannot be earned using investment strategies based on historical prices (also known as weak-form efficiency). The second hypothesis states that all public information is incorporated in the 19

20 price, so fundamental and technical analysis cannot be used for superior gains (also known as semi-strong efficiency). The third hypothesis states that all information, both private and public is reflected in the price, hence no excess return can be made (also known as strong efficiency). Thus according to the EMH this research is pointless as markets are efficient and thereby no strategies can be developed to earn an abnormal return. However as for instance Jensen and Meckling and Akerlof demonstrated the existence of asymmetric information and agency costs means that markets perhaps are not fully efficient (Jensen and Meckling 1976, and Akerlof, 1970). An argument that is further supported by the irrational behavior as documented by Behavioral Finance (see Shleifer, 2000). Thus currently there is an academic debate whether markets are efficient or not. The view of the thesis is that both paradigms have its valid points. In other words instead of markets being a 100 percent efficient this research believes in markets that might be percent efficient. Consequently this research is considered legitimate. 4.2 Electricity Price-behavior Literature The empirical findings on price behavior on the electricity market have its theoretical foundation in the theory introduced above. Much of the cited theory above is often thought of and related to the behavior of stock prices; however researchers have shown that it can also be used in modeling commodity prices. (e.g. Binroth et al. 1979). Electricity as a commodity is unique, as it must be generated and used simultaneous, which means that it is non-storable. Thus once generated, it travels along the transmission grids according to Kirchhoff s law, i.e., following the path of least resistance, and at the speed of light. Hence regardless of how a market is organized a function for balancing supply and demand of electricity must exist. The uniqueness of electricity prices has lead to several characteristics as identified below (see Wolak, 1999, Johnson and Barz, 1998, Lucia and Schwartz, 2002): 20

21 Daily, weekly, yearly seasonal cycles High volatility Frequent price spike Non-normality Leptokurtic Mean reversion Seasonality is normally explained by that prices are influenced by demand, business activities and weather conditions. The high volatility, price spikes, non-normality, and leptokurtosis behavior is generally explained by that electricity is unstorable and the dominance of hydro power in the Nordic market. Mean reversion is generally explained by that increased demand causes prices to increase and more expensive generators have an incentive to enter the market as explained in the theoretical background. Similar a decrease in demand will cause prices to decrease, and expensive generators will leave the market, hence mean reversion seems likely. Another possible explanation for the observed mean-reversion is that it reflects weather condition, which is known for being cyclical and mean reverting (Knittel and Roberts, 2001). However regardless of the reason for the observed phenomenon the existing literature mostly present models where prices are mean reverting, (see Lucia and Schwartz, 2002 and Knittel and Roberts, 2001), but there are also some academics that claims the opposite (see De Vany and Walls, 1999, and Leon and Rubia, 2001). Statistical approaches taken in capturing the characteristics of electricity prices include discrete time series models such as GARCH (see Bunn, 2004, Duffie 1998, Goto, 2003, Knittel 2001, and Longstaff and Wang 2004, ), Markov regime-switching models (see Worthington and Kay-Spratley 2003), continuous-time diffusion models such as meanreversion (see Lucia and Schwartz 2002, Tseng and Barz 2002, and Clewlow and Strickland 2000), jump-diffusion (see Clewlow and Strickland 2000), and other diffusion models (see Deng and Jiang 2002). 21

22 5. Forecast Methodology and Method The literature review has been the foundation for building an appropriate forecast methodology and method. 5.1 Forecast Methodology The natural starting point of any research is the construction of a logical sequence of steps and identification of justifiable method that enables a thorough and reliable analysis. In order to forecast electricity prices it is essential to develop a framework, which can be applied to reach a sound conclusion. Illustrated in figure 5.1 are the three parts, which will constitute the natural flow of the research while answering the research problems, set forth in the statement of problem. The first part aims at creating a forecast framework. The framework contains a description of Nord Pool and a technical and fundamental analysis 10. The second part will then use the developed framework as the foundation for the forecast. This means that the explanation of Nord Pool together with the technical analysis will form forecast models from now on referred to as the technical forecast models. In addition it also means that the explanation of Nord Pool together with the fundamental analysis will form forecast models from now on referred to as the fundamental forecast models. Lastly the framework will be used in developing forecast models, which utilizes the knowledge from both the technical and fundamental analysis; hence the two approaches are merged. The final part of the research will involve reflecting on the models application and usability before the final comments are made in the conclusion. 10 The technical and fundamental analysis will be explained in more detail in section

23 Figure 5.1 Methodology of the Research 5.2 Forecast Methods When predicting the price of any assets there are two theoretical paradigms. The first paradigm is the technical analysis, which claims that past prices behave in predictable manners which can be exploited for forecasting purposes. The Box-Jenkins methodology identified in the literature review has its validation and origin in the technical analysis. The second paradigm is the fundamental analysis, which claims that prices can be estimated by analyzing all other factors believed to have an impact on the exogenous variable. This paradigm has its origin from Graham and Dodd as identified in the literature review. Academics debate whether the technical- and fundamental analysis are substitutes or compliments. The approach undertaken in this research is that they can be considered compliments (for more on this discussion see for instance, Bettman et al., 2006). The research will use time series analysis to extract meaning out of past prices and influential fundamental factors as identified by the technical and fundamental analysis. The objective with time series analysis is to detect patterns that can be exploited in forecasting future values. The assumption of time series analysis is that the distribution of a variable examined is comparable to the distribution of the future, this enables predicting the future of the variable. When applying the time series tools the research will use a two step approach as identified below, for presenting the research models: 23

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