Correlation and Regression Analysis: Applications for Industrial Organizations 1774071584, 9781774071588

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CORRELATION AND REGRESSION ANALYSIS: APPLICATIONS FOR INDUSTRIAL ORGANIZATIONS

CORRELATION AND REGRESSION ANALYSIS: APPLICATIONS FOR INDUSTRIAL ORGANIZATIONS

Ivan Stanimirović

ARCLER

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www.arclerpress.com

Correlation and Regression Analysis: Applications for Industrial Organizations Ivan Stanimirović

Arcler Press 2010 Winston Park Drive, 2nd Floor Oakville, ON L6H 5R7 Canada www.arclerpress.com Tel: 001-289-291-7705 001-905-616-2116 Fax: 001-289-291-7601 Email: [email protected] e-book Edition 2020 ISBN: 978-1-77407-379-7 (e-book) This book contains information obtained from highly regarded resources. Reprinted material sources are indicated and copyright remains with the original owners. Copyright for images and other graphics remains with the original owners as indicated. A Wide variety of references are listed. Reasonable efforts have been made to publish reliable data. Authors or Editors or Publishers are not responsible for the accuracy of the information in the published chapters or consequences of their use. The publisher assumes no responsibility for any damage or grievance to the persons or property arising out of the use of any materials, instructions, methods or thoughts in the book. The authors or editors and the publisher have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission has not been obtained. If any copyright holder has not been acknowledged, please write to us so we may rectify.

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ABOUT THE AUTHOR

Ivan Stanimirovic gained his PhD from University of Niš, Serbia in 2013. His work spans from multi-objective optimization methods to applications of generalized matrix inverses in areas such as image processing and computer graphics and visualisations. He is currently working as an Assistant professor at Faculty of Sciences and Mathematics at University of Niš on computing generalized matrix inverses and its applications.

TABLE OF CONTENTS

List of Figures ........................................................................................................ix List of Tables .........................................................................................................xi Preface........................................................................ .......................................xiii Chapter 1

Introduction and Objectives ..................................................................... 1 1.1. Introduction ........................................................................................ 1 1.2. Objectives .......................................................................................... 2 1.3. The Study ............................................................................................ 3 1.4. Structure Labor ................................................................................... 3

Chapter 2

Theoretical Background ............................................................................ 5 2.1. Introduction ........................................................................................ 5 2.2. Amortization System Constant (ASC) ................................................. 16 2.3. French System of Price Amortization (FSA) ........................................ 17 2.4. Comparative Analysis of ASC And FSA Methods ............................... 17 2.5. American System of Amortization (ASA) ........................................... 18 2.6. Application In Net Present Value....................................................... 19 2.7. Mathematical Models In E-Business .................................................. 20 2.8. Mathematical Design of E-Business................................................... 50 2.9. Product Design And Pricing Policy.................................................... 57 2.10. Using Mathematics To Generate Captive Customers........................ 62 2.11. Development Of Client Networks ................................................... 66 2.12. Mathematical Models In Capital Management ................................ 71 2.13. Cash Management ......................................................................... 73 2.14. Who Is Responsible For Managing Cash Flow? ............................... 75 2.15. The Four Basic Principles For Effective Management ....................... 75 2.16. Operation In Practice of Effective Management of Cash .................. 76 2.17. Cash Conversion Cycle ................................................................... 77

2.18. Models of Demand For Cash Transactions ....................................... 78 2.19. Baumol Model ................................................................................ 78 2.20. Cash Management Miller-Orr Model ............................................. 79 2.21. Commercial Discounts ................................................................... 80 2.22. Inventory Control ............................................................................ 81 2.23. Model EOQ ................................................................................... 82 2.24. Discounts For Wholesale ................................................................ 83 2.25. Inventory Control With Uncertainty ................................................ 83 2.26. ABC Inventory Control System ........................................................ 85 2.27. MRP Systems Subject (PNM) ........................................................... 85 2.28. Inventory Systems Just In Time (JIT) ................................................. 85 2.29. Accounts Receivable Management ................................................. 87 2.30. The Decision Granting of Basic Credit ............................................ 88 2.31. Sources of Credits ........................................................................... 89 2.32. The Five C Credit ............................................................................ 90 2.33. Accumulation Accounts Receivable ................................................ 91 2.34. Short-Term Financing ...................................................................... 91 2.35. Cost of Capital And Its Implications From Business Investment........ 97 2.36. Capital Cost .................................................................................... 97 2.37. Costs of Sources of Capital.............................................................. 97 2.38. Cost of Capital ................................................................................ 98 2.39. Average Cost of Capital ................................................................... 98 Chapter 3

Analysis ................................................................................................. 117 3.1. Presentation of Data ....................................................................... 117 3.2 Exploratory Factor Analysis .............................................................. 122 3.3. Results Filters .................................................................................. 123 3.4. The Economic Cycle and Common Factor....................................... 129

Chapter 4

Conclusions ........................................................................................... 187 Index ..................................................................................................... 193

viii

LIST OF FIGURES Figure 2.1. The logistic curve Figure 2.2. Total cost function Figure 2.3. Average cost functions and marginal Figure 2.4(a). Total cost function of long-term production Figure 2.4(b). Balance coordination costs Figure 2.5. Internal coordination costs Figure 2.6. Effect of economies of scale demand Figure 2.7. Capture cycle Figure 2.8. Compatibility v/s performance Figure 2.9. Benefit of a marketing strategy Figure 2.10. Cash conversion cycle Figure 2.11. Characteristics of the cycle times of some metals prices Figure 2.12. Prices of Commodities in Time Figure 2.13. Intensity of use of some metals in China Figure 2.14. Factors affecting commodity price Figure 2.15. Components of each series cyclic rates Figure 2.16. Components Real Super Cycle and first principal component Figure 3.1. Commodity monthly prices. Period 1971–2007 Figure 3.2. Commodity Price and Components Hodrick Prescott. Aluminum and copper (Monthly Series) Figure 3.3. Commodity Price and Components Hodrick Prescott. Zinc (Monthly Series) Figure 3.4. Interest Rates OECD countries and China (Monthly Series) Figure 3.5. Real and Dear Common Factor (Differences) (Monthly Series) Figure 3.6. Annual Growth Rates of Production Mine Copper. Chile and the world

ix

Figure 3.7. Relevance of Chilean copper production (Percentage of Total World) Figure 3.8. Correlation graphs Rates (1/2) (Monthly Series) Figure 3.9. Correlation graphs Rates (2/2) (Monthly Series) Figure 3.10. Histograms of the data series (Annual Series) Figure 3.11. Correlation graphs Rates (1/2) (Annual Series) Figure 3.12. Correlation graphs Rates (2/2) (Annual Series) Figure 3.13. ACF and PACF aluminum and copper (Monthly Series) Figure 3.14. ACF and PACF tin and lead (Monthly Series) Figure 3.15. ACF and PACF Zinc (Monthly Series) Figure 3.16. ACF and PACF aluminum and copper (Annual Series) Figure 3.17. ACF and PACF tin and lead (Annual Series) Figure 3.18. ACF and PACF Zinc (Annual Series) Figure 3.19. Transformed data. Monthly prices for each commodity. Period 1971–2007 Figure 3.20. Transformed data. Annual prices for each commodity. Period 1971–2007 Figure 3.21. ACF and PACF transformed data. Aluminum and copper (Monthly Series) Figures 3.22 and 3.23. ACF and PACF transformed data. Tin and lead (Monthly Series) Figure 3.24. ACF and PACF transformed data. Zinc (Monthly Series) Figure 3.25. ACF and PACF transformed data. Aluminum and copper (Annual Series) Figure 3.26. ACF and PACF transformed data. Tin and lead (Annual Series) Figure 3.27. ACF and PACF transformed data. Zinc (Annual Series) Figure 3.28. Test R/S (Monthly Series) Figure 3.29. Test R/S (Annual Series)

x

LIST OF TABLES Table 2.1. Types of e-Business Table 2.2. Rules for Different Relations Table 2.3. Examples planning to coordinate relations Table 3.1. Basic Statistics Prices (Monthly Series) Table 3.2. Summary of the Data Applied Tests (Monthly Series) (1/2) Table 3.3. Summary of the Data Applied Tests (Monthly Series) (2/2) Table 3.4. Exploratory Factor Analysis (Monthly Series) Table 3.5. Part of the Variance Explained by Each Factor (Monthly Series) Table 3.6. Correlation Between Factors and Prices (Monthly Series) Table 3.7. Correlation Between Prices and Cycle Components and Trend HodrickPrescott (Monthly Series) Table 3.8. Correlation Between Prices and Periods Bandpass Components (Monthly Series) Table 3.9. Results Tests Components Stationarity Bandpass Filter (Monthly Series) Table 3.10. Correlation between Macroeconomic Indicators Metal Prices (Monthly Series) Table 3.11. Correlation Between Macroeconomic Indicators and Common Factor (Monthly Series) Table 3.12. Regression Results Common Factor with Macrovariables (1). Monthly Serie Table 3.13. Factor with Macroeconomic Variables (2) (Monthly Series) Table 3.14. Correlation Between Components Hodrick-Prescott Filter. Prices and Variables. Macroeconomic (Monthly Series) Table 3.15. Correlation Between Factors and Prices (Monthly Series), January 1971– January 1981 Table 3.16. Correlation Between Factors and prices. Series Monthly, February 1981– February 1991 Table 3.17. Correlation Between Factors and Prices. Series Monthly, March 1991– November 2006

Table 3.18. Correlation Between New Macroeconomic Indicators and Common Factor. Quarterly Series Table 3.19. Factor With Macroeconomic Variables. Quarterly Series Table 3.20. Correlation Coefficient Prices (Monthly Series) Table 3.21. Correlation Coefficient Prices (Annual Series) Table 3.22. Results Price Unit Root Tests (Monthly Series) Table 3.23. Basic Statistics Series Price. Transformed Data (Monthly Series) Table 3.24. Correlation Prices. Transformed Data (Monthly Series) Table 3.25. Results Price Unit Root Tests. Transformed Data (Monthly Series) Table 3.26. Tests for Normality Skewness, Kurtosis and Jarque Bera (Monthly Series) Table 3.27. Normality Tests Skewness, Kurtosis and Jarque Bera (Annual Series) Table 3.28. Tests Heteroskedasticity Waste (Monthly Series) Table 3.29. Tests Heteroskedasticity Waste (Annual Series) Table 3.30. Test of Independence Shift Points and RVN (Monthly Series) Table 3.31. Test of Independence shift points and RVN (Annual Series) Table 3.32. Test of Independence BDS (Monthly Series) Table 3.33. Test of Independence BDS (Annual Series) Table 3.34. Test Hurst exponent Wald (Monthly Series) Table 3.35. Test results Geweke and Porter Hudak (Monthly Series) Table 3.36. Test Results Geweke & Porter Hudak (Annual Series) Table 3.37. Tests of Cointegration Johansen (Monthly Series) Table 3.38. Test Dickey-Fuller Waste Cointegration (Normalized Equation 2) Table 3.39. Test Dickey-Fuller Waste Cointegration (Normalized Equation 3)

xii

PREFACE

In recent years the levels of commodity prices have reached very high values, and industrial metals have played an important role in this boom. The explanation found in the literature is that they are directly influenced by changes in the world economy, so they have a cyclical pattern, with periods of high and low prices. In this book, a study of prices five industrial metals (aluminum, copper, tin, lead, and zinc) is performed. What is sought is to find a relationship between the temporal patterns observed in their prices macroeconomic indicators of global activity. In the case of industrial production indices, interest rates, and exchange rates, macroeconomic variables of seven major OECD countries plus China are used. For this, the econometric tool known as the Kalman filter is used. With it, using a representation called State-Space, a common component at five-price series study, which is postulated is capable of representing the general state of the economy is obtained. This factor is then related to the aforementioned macroeconomic variables, where a regression between the common factor and these indicators are estimated. Furthermore, to sensitize these results, by using the filters Hodrick-Prescott and Bandpass, for each series a trend component and a cyclic component, with the idea to see the relationship between them and the indicators extracted Global economy. Finally, an analysis of the competitiveness of countries rich in mineral resources are encouraged. It aims to raise the discussion of whether to have a diversified metal production causes a particular company and country to achieve a more competitive position in the market for these commodities. The main results show that the prices of commodities considered in the analysis are affected by a common factor to them. Upon relating this factor to macroeconomic indicators not found a significant relationship, which changes when using new representative variables of these economies (GDP and imports of China). The analysis is done with the two techniques to filter the series of prices, results indicating that tin is the metal having the greatest differences with the rest are obtained.

Regarding the discussion on competitiveness, it is proposed that companies with a more diversified resource endowments are more competitive by being able to adopt global strategies, allowing them easier access to scarce resource, land, and ensure their production in the long term.

xiv

1 Introduction and Objectives

1.1. INTRODUCTION In recent years there has been a great cycle in the price of some commodities, which have presented a rare period of high values. According to IMF data, in 2007. The price of copper rose by 357% annually compared to 2002, and aluminum 95% over the same period (nominal values). This book seeks to estimate the impact of various macroeconomic variables in the price of certain metals, in order to have a study that shows quantitatively how the international situation affects the market value of these minerals. This is particularly important for Chile, which has an economy heavily based on the export of these resources. You have studies that indicate the ways in which they can be affected will always be useful, as a source of information that can be used to take the necessary measures once the relevant variables identified. Commodities are characterized by periods of ups and downs in your quote. One explanation for this is the existence of demand shocks, which face an inelastic supply (at least in the short term), it causes an increase in the price level. Then, once the deal is set to increased demand, reduce pressures on prices, allowing them to come back to its long-run equilibrium. Independent of this, it is interesting to note that some metals show similar trends in the evolution of their market values. Therefore other factors that have a common impact on all of them and that affect the temporal pattern of their contribution should be. These factors can think interest rates of economies, the level of production in them,

Correlation and Regression Analysis: Applications for Industrial Organizations

2

There is a wide variety of economic studies related to the issue of price behavior of metals and their variability. Moore (1980, 1988) conducted a study of the influence of the economic cycle in price by analyzing common factors. The short-term movements in prices attributed to the inelasticity of supply, which causes prices are most exposed to the demand, which in turn reflects macroeconomic effects (Davutyan and Roberts, 1991; Grilli and Yang, 1981; Labys al., 1998 and Slade, 1981). In this study the work of Labys, Achou and Terrace (1999) is followed. In their research, the authors analyze the existence of factors specific to each metal and a common factor (which explains why metals commodities prices show similar trends). Then relate this factor variables indicative of the global economic cycle. The most important results obtained by these authors are the common factor explains between 71% and 16% of the variance of the metals considered in their study. Specific factors in turn account for between 81% and 63% thereof. Furthermore, the effect of industrial production is extremely important, while the other variables have a much lower incidence. Metals considered in this study are aluminum, copper, tin, lead, and zinc, each of which is traded on the London Metal Exchange. Data are monthly prices from January 1971 to May 2007. The economic variables chosen for the study are the level of industrial production, interest rates and exchange rates. These data are obtained from the International Monetary Fund (IMF), which delivers an annual inventory statistics for the global economy.

1.2. OBJECTIVES 1.2.1. General Purpose •

Conduct a study about the behavior of the prices of some mineral commodities according to the international economic cycle where rapid growth in global activity and other variables were behind the sharp increase was the price of some metals to the third quarter of 20061. It seeks a quantitative assessment of the impact of these macroeconomic variables on the prices of these metals.

1.2.2. Specific Targets •

Study the existence of common factors that may justify similar patterns seen in the trend of prices of commodities considered.

Introduction and Objectives

3

•

Quantify the impact these have on this macroeconomic variables. And see what is the relative importance each. • Finally, from this book we seek to motivate an interesting topic to deal with in greater depth and analyzed here only in general terms: competitiveness of countries rich in mineral resources. This from the point of view of whether it is useful to diversify the production base considering the effect that the economic cycle has on prices. An important observation should be made at this point. This is that there are many other variables that influence metal prices beyond economic market conditions, which are representing operating costs. For example, environmental regulations are becoming stronger, making mining operations more expensive. Also it influences aging deposits and technological advancement. Assuming this work movements ceteris paribus economic cycle affect metal prices under study

1.3. THE STUDY The study is expected to indicate or show that macroeconomic shocks affect the price cycle of these commodities, which would explain why they show similarities in the historical movement of prices. Of particular interest in this case is the impact of the growth of China’s economy (its level of industrial production), especially in the case of copper, for among the explanations that have been given to explain its high value, is the great demand for inputs from the Asian country. The main software used in the development of this work is GAUSS 7.0. To obtain relevant statistics and other complementary results the EVIEWS 6.0, STATA 10 software MATLAB 7.0 and GSLIB were also used.

1.4. STRUCTURE LABOR In developing this work series of monthly and annual time they are used. In order not to overload the presentation in the main body of the study and analysis only in the case of commodity prices with monthly data it is presented. In the Attachments section tests performed differentiating when data are used in different frequency are detailed. In the last point of this section results using annual series are given.

2 Theoretical Background

2.1. INTRODUCTION Mathematical models can be classified according to different criteria. •

If the data are affected by chance (which mathematically measured by the odds) model is stochastic. Otherwise, deterministic model is said. • The model will be linear if the functions and conditions are linear, but speaks of nonlinear model. • The continuity of data variables and make the model is continuous, and its opposite the discrete model. As there is a more complete theory under the assumption of linearity and better-adapted numerical methods, linear models are “easier” to solve. Abusive linearization nonlinearities can lead to disastrous results. Stochastic models can receive treatment to return to them deterministic. In recent times, driven by information technology, biology and neuroscience, among others, discrete mathematics have a strong development. Indeed, there are situations where it is better to raise the discrete input and not the continuous model, as they are a better reflection. We must not forget that passing the mathematical model to the numerical model and computational solution is being a discretization. On the other hand, apart from the binary logic (0–1, black-white) has emerged fuzzy logic that can take truth values in the range [0,1] (the full range of gray), and the theory of fractals offer new possibilities to mathematical modeling.

Correlation and Regression Analysis: Applications for Industrial Organizations

6

Companies’ financial information is limited ultimately to relevant information about the situation and development of the economic and financial situation of the company. It can be considered, on the other hand, as a subsystem of “integrated system management information,” i.e., a system that connects all kinds of information produced in the company, such as statistics, forecasting, billing, payroll, accounting, in a joint treatment. In this regard, the progress made in recent years is spectacular thanks to computer resources and tele-informatics existing today. The accounting analysis is an integrated information system within the overall financial reporting system – that is economic accounting. It aims to reading and analyzing information and interpreting the results thereof. This financial information is not made to be hidden, but to be communicated to different recipients (owners or partners Business, Public Administration, Financial Institutions, etc.). The field of accounting knowledge and financial information also covers those techniques pursuing information verification (audit) carried out by independent professionals of the company. Accounting and financial reporting includes within its knowledge and techniques, analysis and interpretation of the information prepared. A bank, for example, not only reads the accounting documentation that provides the applicant for a loan, but interprets it to see whether it will be able to return at maturity. The structure of financial information is related to the goal, to achieve through the operation of various functions within the financial information: • information processing; • communication; • verification (accounting audit); and • analysis and interpretation by the user. It is specifically the task of preparing the coating to be more important since it will involve the result of the remaining functions. During the preparation of accounting information it will be necessary to observe parameters so that this meets the characteristics required: • • •

recognize and identify facts that define accounting information. a measurement in monetary units of such accounting events. a synthesis of information: This section accounting reports among which the most representative are the balance sheet will reflect

Theoretical Background

7

the statement of assets, liabilities and net of the organization at a given time are made, and the Profit that displays the set of income and expenses over a period and according to these economic result for the period and losses. The company is oriented to satisfy market and generate wealth so that financial information should be oriented to the market and generate wealth must report from a financial standpoint on: • Wealth creation. • The return on investment of the partners or shareholders. • Generating cash flow. Wealth generation is known and measured through the income statement. The return on investment of the partners or shareholders is obtained from the information contained in the statements of financial position, performance and changes in stockholders’ equity. The financial information that has value is one that has an impact on our actions, answering our questions, which is based on decision-making as a competitive weapon to help the company drive forward to capture market improve profitability, improve efficiency, etc. The significance of the information is based on the ability to represent symbolically in words (concepts) and quantities results of operations and financial condition. Financial information must first meet internal needs and should be aimed at managers of the company so they can manage, make decisions and achieve goals. Secondly must meet the general needs financial, addressed to stakeholders who are not directly involved with management, and finally must cover fiscal needs. The information must come only from a single source which is the general accounting system. Financial information is essential in making strategic and tactical decisions so their system and intelligent preparation is important so that it can be used as a competitive tool. It should be seen as a product, business support, which provides added value for decision making and should be effective in terms of timeliness. Information should be ordered for each particular company oriented markets, customers and products with which it participates. This way one can measure the company in its economic environment. Financial information is an important tool for analyzing the results of the company source but it is also necessary to know the competitive

8

Correlation and Regression Analysis: Applications for Industrial Organizations

environment in which the company operates, evaluate the marketing system, quality of products, price, quality of staff, etc. Customers are a power group that impose conditions such as a minimum level of service, product location. The price has a pressure in competition and profitability of the company. So the departmental and cost center information is needed so that those responsible can monitor and manage their maximizing their results area. To mediate making a decision, one should plan what one want to do in order to be able to give answers to the questions why and how. If these questions are answered, decisions taken were appropriate, since taking a good decision all those involved in the national economy we will benefit (government, employers, employees, etc.) That said, we must assert ourselves of proper planning. For this reason, it is important to note that planning is a universal activity. Although their content may vary at different levels in the structure of the organization, there are certain steps which always occur that is planned. These steps are similar to those that always hit a process that involves making decisions; then, in a sense, make plans is just a special case of decision-making with a strong orientation towards the future. For this situation it implies anticipate future activities concerning proposed decisions and the future outcome of present decisions. The fact that we make a decision to a problem or action plans should be sought in accordance with the problems and solutions of tomorrow. Forecasts and research conducted carefully are the keys to making an excellent decision because selecting a decision, it must be based on criteria to be valid in the present and in the future. Good decision-making must be based on facts and not on vague and general emotions. The activities are based on situations that dictate the facts, which can avoid obstacles, and should not be avoided, are recognized as existing and included in the plans, along with the respective provisions to deal with them. The facts relevant to the situation considered relate to the experience and knowledge of who uses it. The office of executive decision-making involves a certain degree of financial risk in a strategic framework defined by the company itself and a predetermined economic and social environment. The suitability of these decisions will depend on the preparation, experience, personality and information held by the management.

Theoretical Background

9

In decision-making experience is a key element because decisions must be made on a highly complex reality because of the huge number of variables that come into play. The accumulation of experience is long and costly. If we consider that the more one learn is as a result of mistakes, reaching a high level of experience in the business world can have a terribly high cost. The immediate consequence is that the whole experience to be gained without the effects that might result from an erroneous decision or simply a nonoptimal decision will be well received and cheaper, whatever the cost. It is hardly possible to imagine a field of greater importance for human than decision making. We have a problem when we do not know how to follow. Once we have a problem, take a decision (including doing nothing). We chose an alternative that seems to us rational enough to allow us more or less to maximize the expected value after our resolute action. Quietly issued a control plan that guides us in making decisions, including decisions related to modify that plan control. Finance, long considered as part of the economy, emerged as an independent field of study early last century. Originally they were associated only with documents, institutions and procedural aspects of capital markets. With the 1920s, technological innovations and new industries brought about the need for more funds, promoting the study of finance to highlight liquidity and financing companies. Attention focused instead on internal management in external operation. By the end of the decade it intensified interest in the securities, especially common stock, making the investment banker a figure of special importance for the study of corporate finance period. Depression in 1930s forced to focus the study of finance in the defensive aspects of survival, preservation of liquidity, bankruptcies, liquidations and reorganizations. Conservative tendencies dominated, giving more importance to the company to maintain a solid financial structure. Abuses with debt, especially debt related to the holding utilities, were exposed to many businesses collapsed. These failures, along with the fraudulent way they were treated numerous investors, grown demand for regulations. They increased the financial information that companies should disclose, and this in turn caused the financial analysis was broader. During the 40s finance they followed the traditional approach that had developed during the previous decades. The company is analyzed from the point of view of someone outside it, as it could be an investor, but without putting emphasis on decision-making.

10

Correlation and Regression Analysis: Applications for Industrial Organizations

In the mid-1950s they became important capital budget and considerations relating thereto. New methods and techniques for selecting capital investment projects led to a framework for the efficient distribution of capital within the company. The financial manager now had charge of the total funds allocated to assets and capital allocation to individual assets on the basis of an appropriate acceptance criteria and objective. Subsequently appeared complex information systems applied to finance, which enabled the realization of more disciplined and profitable financial analysis. Was deeply affected electronic means used by companies to conduct their banking, pay your bills, collect the money they are owed, transfer cash, determining financial strategies, manage currency risk, etc. valuation models for use in making financial decisions were devised. The highlight of the 1960s was the development of portfolio theory (Markowitz – 1960, later perfected by Sharpe, Lintner, Fama and others) and their subsequent application to financial management. This theory explains that the risk of an individual asset should not be judged on the basis of possible deviations from expected performance, but in relation to their marginal to the overall risk of a portfolio of assets contribution. Depending on the degree of correlation of this asset with others that make up the portfolio, the assets will be more or less risky. In the 1970s they began to apply the pricing model of capital assets Sharpe for valuing financial assets. The model of the risk implied that the company did not matter to investors of a company because it could dilute the portfolios of shares in its possession. Also caused it to focus even more attention to market imperfections when selecting assets by the company, financing and dividends are judged. Also during this decade, Black and Scholes model formulated pricing options for assessing relative financial rights. The existence of an options market allows the investor to establish a protected position and risk by purchasing shares and, at the same time establishing stock options. Efficient financial markets in performance caused by a position of this type must be a risk-free rate. If this is true, it would be possible to establish exact formulas for valuing different types of options. In the 1980s, there has been significant progress in the valuation of companies in a world where uncertainty reigns. It has placed a growing attention to the effect of market imperfections have on the value. Economic information allows for a better understanding of market behavior that have financial documents. The notion of an incomplete market, where the wishes

Theoretical Background

11

of investors of particular types of values are not met, puts the company in the role of carrying out the marketing of special types of financial claims. In the 90s, finance has had a vital and strategic role in business. CFO has become an active part: the generation of wealth. To determine whether generates wealth must know who provide the capital that the company requires for profit. This becomes the basis of opportunity cost, for which the product will be judged, investment and operating decisions. As global financial markets are increasingly integrated, the finance manager should look for the best price and often-national borders currencies and other aspects. External factors influence every day in the financial manager: deregulation of financial services, competition among capital providers and financial service providers, volatility of interest rates and inflation variability of exchange rates currency reforms tax, global economic uncertainty, external financing problems, speculative excesses and ethical problems of certain financial businesses. In short, the study of finance descriptive study evolved from its early days until the current normative theories rigorous analysis. They have ceased to be a fundamentally concerned about raising funds to cover the field asset management, capital allocation and valuation of companies in a global market. A differential equation is an equation-containing derivative of an unknown function. If this function is real variable, ordinary differential equation (ODE) says, and if the unknown function is multivariable equation is partial derivatives (EDP). The general form of an ODE will represent

F ( x, y, y ', y '', ..., and ( N= ) ) 0,=y f ( x )

(1)

The order of an ODE is the order of the highest derivative. Form (1.1) is a relationship between n + 2 variables, we assume that it is always possible to solve for y (n) in terms of the other variables, giving the normal way:

and ( n ) = f ( x, y, y ', y '', ..., and ( n − 1) )

(2)

ODEs are linear if F is a linear function of the variables y, y ', y '',..., and ( n ). Then they can take the form

Correlation and Regression Analysis: Applications for Industrial Organizations

12

n ( x ) and ( n ) + an − 1( x ) and ( n − 1) + .... + a0 ( x ) and ( n ) = g ( x) Whether the function g(x) is equal to zero speaks of a homogeneous equation and otherwise is the inhomogeneous equation. Recall that given a differential equation have the following problems: • • •

existence of the solution; uniqueness of the solution; calculation of the solution (analytical methods) or a “proxy” it (numerical methods). The variable differential equations here noted x, may be the time noted t, in which case the event is a dynamic phenomenon. In turn, it may be necessary to determine whether the behavior is periodic. Moreover, the equations can acknowledge a time shift-giving rise to equations with delay. If the equation depends only on spatial variables speaking of autonomous equations. Besides equation, in practice must impose additional conditions that may be starting or edge (or boundary). In most cases it is impossible to represent the solution analytically (using formulas). The same equation can give information on the characteristics of the solution. What matters is the long-term qualitative behavior; for example, for a population it is important to determine if they maintain or tend to disappear. Some models may require not one but several equations, i.e., a system. An interpretation of the derivative as its sign corresponds to the growth of the function in the positive case, or decrease if the sign is negative. This enables the first order differential equations to describe chemical reactions of decomposition, populations or economic growth. As the number of individuals of a population is whole, it seems impossible in principle to use differential equations to describe their growth. So we must assume that large populations change continuously differentiable with respect to time. We denote p(t) of a given population at the time t, and p denotes the difference between birth rates and mortality population. We also assume that the population is p0 at time t0. • Act Malthus Growth Under the assumption that the population is isolated, i.e., there is no emigration or immigration, the rate of population change is proportional to the population at that time.

Theoretical Background

13

(3) In the simplest model, Malthus believed that r (t, p) is equal to a constant, i.e., r does not depend on time or population. In this case the solution of initial value problem is:

p (t ) = p0e a ( t − t 0 )

(4)

The growth is exponential over time. This model is unreasonable for the human population, but is well suited to some small rodents. • Act Logistics Population Equation (3) does not realize competition develop together individuals of the same population for the limited living space, natural resources and food available. One have to add a name given by –bp2, where b is a constant competitive term, as the statistical average number of encounters per unit time is proportional to p2. Then we have to solve the initial value problem: ,

p (t0 ) = p0

(5)

This equation is known as the logistic law of population growth and b coefficients will be vital coefficients it says. The solution of Eq. (5) by separation of variables is (6)

Let’s examine the type of population that predicts. When t → ∞ we have that That is, regardless of the initial value the population always tends to the limit value a/b. An analysis of the second derivative of p(t) we conclude that is increased if p ( t ) < a / 2b and

is decreasing if p ( t ) > a / 2b .

Figure 2.1 shows the logistic curve (at S) if p0 t

Asy. stderr

z (H0: d = 0)

P> z

· Aluminum

.5

21

-.064772

1428

-0.4537

0.656

1,812

-0.3574

0.721

· Copper

.5

21

024039

1527

.1574

0.877

1,812

.1326

0.894

· Tin

.5

21

065997

2158

.3058

0.763

1,812

.3642

0.716

· Lead

.5

21

-.054025

2041

-0.2647

0.794

1,812

-0.2981

0.766

· Zinc

.5

21

-.103786

1494

-0.6946

0.496

1,812

-0.5727

0.567

182

Correlation and Regression Analysis: Applications for Industrial Organizations

Annual series Table 3.36: Test Results Geweke & Porter Hudak. Annual Series Power

ords

is d

stderr

t (H0: d = 0)

P> t

Asy.

z (H0: d = 0)

P> z

stderr

· Aluminum

.5

7

-.257169

3774

-0.6814

0.533

.443

-0.5805

0.562

· Copper

.5

7

470173

4845

0.9704

0.387

.443

10,612

0.289

· Tin

.5

7

955894

2237

42739

0.013

.443

21,576

0.031

· Lead

.5

7

225413

7547

.2987

0.780

.443

.5088

0.611

· Zinc

.5

7

824819

6455

12,778

0.270

.443

18,617

0.063

A.3. Tests of Series Multivariate Cointegration Analysis Durbin Watson tests and Engle & Granger It is said that two variables are cointegrated if they have the same order of integration and error process that forms including regression (in levels, i.e., untransformed variables), is stationary. Thus, there is a relationship of long-term balance between the variables, while the short-term deviations that may exist between them are stationary. Now cointegration tests Durbin Watson and Engle & Granger performed. The equations used to estimate residues are (series in logarithms): DW test is the simplest to analyze whether cointegration between variables. This test is used to see if the residuals of the regression are stationary. The null hypothesis is accepted in case the DW value is zero. If its value is high, the hypothesis is rejected, indicating that there is cointegration. To test Engle & Granger previous regression with each series of price as the dependent variable is performed. We proceed in this way because a priori there is no information about which of the waste generated by these five regressions is the most appropriate. Then, using Dickey-Fuller examines whether the residues of the equation

Analysis

183

are stationary. If the wastes are non-stationary (i.e., the null hypothesis of the presence of unit root DF is not rejected), it is concluded that the series are not cointegrated. It is important to note that the critical values are not the same DickeyFuller test standard. In this case the values indicated by Enders (2004) are used. It may be that the regressions shed conflicting results. This may be the case that only one group of the variables are cointegrated, and considering all regression would not reveal this relationship cointegration. (For this reason in the following point test Johansen is enhanced). Thus, the first above equation is estimated at 5 times, with each set of prices as a dependent variable. The results are shown in the following tables, where in each case is presented first typical results of the regression and second test unit root residues. With monthly series, DW test does not reject the null hypothesis of no cointegration. Applying Engle & Granger and make the Dickey-Fuller, the presence unit root aluminum, tin and zinc it is not rejected. Instead, lead and copper reject the hypothesis that residues are stationary, so in this case no evidence of cointegration. It is also concluded that for annual series DW test rejects the null hypothesis of no cointegration. The test of Engle & Granger does allow accepting the null hypothesis with variations depending on the chosen level of significance. As the case with monthly series, it is more difficult to accept that the series are not cointegrated in the case in which copper and lead are used as dependent variables.

Monthly series Included observations: 432 after Adjustments Trend assumption: Linear deterministic trend Lags interval (in first Differences): 1 to 4 Unrestricted Cointegration Rank Test (Trace) Table 3.37: Tests of Cointegration Johansen. Monthly Series Hypothesized No. of CE (s)

Eigenvalue

Trace

0.05

Statistic

Critical Value

Prob. **

184

Correlation and Regression Analysis: Applications for Industrial Organizations

None

0.069332

64.78722

69.81889

.1180

At most 1 At MOST 2 At MOST 3 At MOST 4

0.039675 0.026157 0.008203 0.002889

33.74699 16.25795 4.807867 1.249708

47.85613 29.79707 15.49471 3.841466

.5157 0.6940 .8289 .2636

Trace indicates no Cointegration test at the 0.05 level * Denotes rejection of the hypothesis at the 0.05 level. ** MacKinnon-Haug-Michelis (1999) p-values. Table 3.38: Test Dickey-Fuller Waste Cointegration (Normalized Equation 2) t-Statistic

Prob. *

Augmented Dickey-Fuller test statistic

-2.649406

.0928

Test critical values:

1% level

-5.017000

5% level

-4.324000

10% level

-3.979000

* MacKinnon (1996) one-sided p-values. t-Statistic

Prob. *

Augmented Dickey-Fuller test statistic

-4.461363

0.0011

Test critical values:

1% level

-5.017000

5% level

-4.324000

10% level

-3.979000

* MacKinnon (1996) one-sided p-values.

For the first regression (D.1.2.8) the null hypothesis is not rejected. In the second case it is not accepted 5% and 10%.

Analysis

185

Table 3.39: Test Dickey-Fuller Waste Cointegration (Normalized Equation 3) t-Statistic

Prob. *

Augmented Dickey-Fuller test statistic

-2.387459

.1522

Test critical values:

1% level

-4.592000

5% level

-3.915000

10% level

-3.578000

* MacKinnon (1996) one-sided p-values. t-Statistic

Prob. *

Augmented Dickey-Fuller test statistic

-4.544274

0.0009

Test critical values:

1% level

-4.592000

5% level

-3.915000

10% level

-3.578000

In this case it is not possible to reject the existence of a unit root. Only if (D.1.2.11) is rejected at 5% and 10%. 10% the null hypothesis is rejected in the latter case (A.3.20).

Causality Analysis Test Granger Causality In a bivariate case to take two stationary variables. Note that the statement “Granger cause X to Y” does not have the traditional meaning of causality, i.e., does not mean that Y is a result of X, only measures informational content. It is also possible to test the Granger Causality for multivariate case.

4 Conclusions

In the first part of the work, it was done an analysis of the behavior of the price series, in order to verify whether governed according to the specifications in the literature. First, the correlation between the prices of metals is higher when working with annual series, which occurs both for data and for return levels (first difference of logarithm). For monthly and annual data cannot reject the existence of a unit root when considering the series in levels. The other series are stationary when using transformed data. After applying the battery of tests, results are obtained as expected according to previous studies. With the idea of getting a first impression about a common component in these five series analyzed, Exploratory Factor Analysis was performed. The idea of this technique is to find some (os) pattern (s) in the relationship between the variables under study, in particular, looking to see if these variables (observed) can be explained in terms of a smaller number of variables called factors. It is known that this type of analysis has some drawbacks (e.g., the weights of the factors are not unique), but it is easy to implement and is useful as a preliminary test. Their results show that using two common factors (or latent variables), in the case of annual data they can explain 80% of the total variance of the series, from 57% for tin to 99% for copper. When working with monthly data, the results are between 44% tin and 98% for copper, reaching account for 76% of the total price variation. While this is not the aim of this study, its results give an overview of the differences between the various price series with which you work, where tin, which has an overall much higher than other variance (near twelve times that of copper), it has a much more important than the other metals specific component.

188

Correlation and Regression Analysis: Applications for Industrial Organizations

With the Kalman filter, by a representation state-space dynamic model factors was used, from which is “extracted” a common factor to all price series with specific factors each time. The common factor which seeks to represent is the general state of the world economy, and thus this indicator is associated with the movement of commodity prices in the period. In this case, when working with monthly series, the results indicate that the estimated common factor explains the variance of the metals from 13% in the case of tin to 53% for lead. Specific factors account for an even higher percentage between 47% for lead and 87% for tin. When annual data are used, the results show some differences with the previous case. Again specific factors may justify most of the variability in prices, between 44% for lead to 88% for tin. In turn, the common factor is in the range 12% to 56% for tin and lead, respectively. Regarding macroeconomic variables used, it is interesting to note the high correlation between industrial production indices (excluding China) among the countries considered. With interest rates the trend is similar, and exchange rates mixed results presented correlations with positive and negative values mostly are considerable. Following the trend with previous results in the analysis of the price series, the statistical correlation is greater when considering data less frequently. When calculating the correlation between macroeconomic variables and the common factor it is the same trend as they show with prices. Interest rates and generally have low negative values, exchange rates show varying signs and industrial production indices also have low values. By using annual data results show no significant changes. As he left established in chapter objectives, should make an important observation before attempting to explain these findings or conclusions obtained by the purely economic side. First, it should be noted that mineral deposits are of discrete nature. New exploration campaigns may find interesting deposits that were previously unknown and did not affect production and total supply of the metal in question. In addition there has been a progressive change in environmental constraints which are increasingly stringent and often they prevent the activity. It should also be noted the critical role of energy in the cost of mining operations (becoming more expensive to carry out an operation and as an example just think of the use of water). All these variables have an effect on metal prices, and the previous analysis is simply assumed that they respond to market fluctuations

Conclusions

189

and most demanding economies. Bear in mind that in interpreting the results, since this part also plays an important role in increasing prices of commodities analyzed. The results indicate that macroeconomic variables chosen not affect the variable that represents the international economic cycle (obtained from the dynamic model). two regressions for the common factor, the first based on the aggregate index of industrial production (consider the set of countries used in the study) and interest rates, and the second function only index industrial production (both regressions are estimated series with first differences). The results show that in the first equation the industrial production index has marked impact on the common factor to be monthly data, it must-have no significant effect. Interest rates have less relevance, and except China, are also significant. For the second regression the effect of industrial production is not significant. By using annual data have similar results, but in the second regression aggregate index industrial production is significant and its associated coefficient is higher than the monthly case. Interestingly, the autoregressive coefficient is important in both frequencies, being significant to ignore interest rates in the regression. This is because when considering average data, they give a smoother image, therefore the evolution of prices is more smoothly and has less variability in the period. This is consistent with the statement made by Palaskas and Varangis (1991), who argue that with high frequency data (in this case monthly data), the explanatory power of macroeconomic variables is less than when considering low frequency data (annual). The fact that tin is the metal that has more difference with the rest is reinforced by sensitizing analysis using filters Hodrick-Prescott and Bandpass. With each a trend component and a component representing the cycle of each series analyzed is obtained. Tin is the only commodity that has a negative correlation in the trend component in the aggregate index of Industrial Production (levels). Here has not tried to make a comparison between the two filters, but these effects could (since in a series never known exactly what the cyclic part and what is the trend) create a series as the sum of two components and after applying the filters analyze what that gives the most similar to the components of the original series values. Another way to do this would be to compare the results truncating the series. Thus, each first filter is used considering the entire series. Later the same analysis is done but using less data (cutting the series in recent periods). Finally you can compare which

190

Correlation and Regression Analysis: Applications for Industrial Organizations

one component of the truncated trend towards the end of the sample is more similar to that obtained with the complete series. All this indicates that the cartel formed by the producers of tin (ITC) may have played a role in the eighties. Furthermore if one considers that by extending the analysis and separating the sample data into three subsamples is that tin prices differ substantially only in this period, and for the other two subsamples (pre- and post-eighties), prices behave quite similar to other commodities that are considered at work. It would be interesting to have more in-depth studies (such as the industrial organization of markets), which reflects the differences between each metal that has been used in this research. On the other hand, industrial production data that were used to represent China’s economy are quite erratic, so the results reflect this and in no case downplay the fact that its economy has had on commodity prices, as it is indicated by the recent literature. By using quarterly data for a subsample of the data series and other macroeconomic variables (such as total demand from China), you get some of them are indeed significant to explain the common component price series. This indicates that the variables used initially may not reflect in the best way the impact of the most important economies in the price of metals analyzed. In this must have played a role also the fact that data are often less than the monthly data used initially. The metal prices have cycles, with periods of high and low values. Due to the different structure in their markets, some of them show a similar behavior to changes in the global economy. If they all were affected in the same manner and magnitude of the economic cycle, the fact of having a diversified production of industrial mineral resources would not be useful to prevent income from being affected by this behavior, but nevertheless the fact of having the option of investing in different deposits allow each company to be more competitive than those that base their exports on a single commodity. This is because it may be the case that a company is able to adopt global strategies find an attractive deposit precious metals or precious stones (gold or diamond for example), those with more stable prices over time, and in this case the above would not. In addition, beyond focus the analysis on the behavior of prices of resources exploited, for a mining company is decisive competitive access to mineral reserves that ensure and sustain the supply. It seeks access to resources to ensure that operations continue in the future (it’s non-renewable resources). To advance competitiveness, companies need to

Conclusions

191

ensure access to scarce resource, in this case, land. That’s what makes the difference. In this sense, there is a clear difference between the types of private or public companies. Multinational mining companies have access to resources in different regions of the world, while domestic firms face restrictions on access to resources outside the national territory, representing a distinct disadvantage by not being able to adopt global strategies. So, although you cannot judge the competitiveness of a determined by the quantity and quality of resources it has (since these are determined by nature) country, if they can make comparisons between mining companies owned and capacity invest and access resources globally. It is thought that if a country with tradition and experience in the extraction of these resources accomplishes this.

INDEX

B

A Abrupt change 131 Actual Windows Microsoft 45 Administrative personnel 24 Affiliate program 40 Agents acquire 132 Alternative mechanism 31 Alternative technology 70 Aluminum 117, 121, 126, 133, 147, 148, 149, 155, 157, 181, 183 Amortization 15, 16, 17, 18, 97 Annual data 187, 188, 189 Annual data analysis 123 Annual inventory 2 Anticorrosive metal 149 Asset resource 56 Autocorrelation 154, 155, 159, 164 Automobile assembly 44

Behavior 2

C Capital accumulation 18 Capital budget 10 Capital management 71, 72 Cash generation 73 Cash management 76, 78, 79 Commercial credit 91, 92 Compound interest criteria 15 Computer application 22, 51 Concurrency restriction 31, 33, 35 Cost information 43 Critical mass 21, 50, 68, 70 Critical value population 14 Customer behavior 58

194

Correlation and Regression Analysis: Applications for Industrial Organizations

D Data analysis 133, 154 Database administrator 71 Decision-making 7, 8, 9, 43 Deterministic 5, 116 Digital distribution 27 Digital product 22, 24, 27, 28, 29 Dynamic analysis 126, 129, 133

E Econometric techniques 34 Economic environment 7 Economic growth 12, 146, 147 Economic market 3 Electronic auction 22 Electronic commerce process 56 Electronic market media supply 22 Electronic version 60 Equilibrium 15, 106 Evolutionary approach 68 Explicit communication 30

F Financial analysis 9, 10 Financial asset 10 Financial businesse 11 Financial domain 19 Financial impact 18 Financial information 6, 7, 9, 22, 58 Financial management 10, 37, 73 Financial manager 10, 11, 73, 97, 98 Financial risk 8, 97 Financial strategies 10 Financial System 15 Financial transaction 19 Financing operation 15 Frequency 3 Frequency data 189

G Global activity 144 Global economy 117, 122, 123, 144 Global financial markets 11 Global macroeconomic 126 Global market 11 Gross Domestic Product (GDP) 121 Growing international connectivity 144

H Homogeneous 12 Human allocator 32 Hypothesis 118, 119, 120, 121, 124, 129, 136, 165, 170, 171, 172, 175, 182, 183, 184, 185

I Immediate consequence 9 Immigration 12 Industrial economy 20, 24 Industrial metal 132, 144 Industrial production 122, 131, 132, 133, 136, 137, 138, 188, 189, 190 Information economy 20, 48, 49, 51 Information product 59, 60, 62 Information technology 5, 31, 32, 34, 51 Infrastructure development 146 Installment 16, 95 Integrated information system 6 Intelligent enterprise 56 Intelligent preparation 7 Intermediate depreciation 18 Internal Rate of Return (IRR) 19 International Monetary Fund (IMF) 2 Internet distribution 27

Index

Internet service 61 Internet technology 24, 29, 37, 39, 40, 44, 55, 57 Interpretation 6, 12, 26 Interpretations economic 14 Inventory management 21, 55 Investment 7, 9, 10, 11, 14, 15, 19, 43, 47, 63, 64, 65, 68, 87, 88, 89, 97, 100, 102, 103, 104, 113

J Just in time (JIT) 85

K Knowledge management, 56

L Liquidity 9, 71, 72, 73, 89, 93, 108 Logistic curve 13, 14

M Macroeconomic 1, 2, 3 Market efficiency 21 Market improve profitability 7 Market information product 40 Marketing approach 27 Marketing system 8 Market structure 28, 29 Material Requirements Planning (PNM) 85 Mechanism 34, 35, 39, 61, 88, 111 Mediate 8 Miscommunication 43 Molybdenum 146 Monitoring technology 32, 34 Multi-player strategy 65 Multivariable equation 11

195

N National territory 144, 191 Natural resource 144 Net Present Value (NPV) 19, 88

O Online auction 20 Online customer behavior 28 Optimum production 26 Ordinary differential equation (ODE) 11 Organizational function 32 Organizational structure 39 Organization for Economic Cooperation and Development (OECD) 121

P Partial autocorrelation (PACF) 155 Performance software 67 Periodic disbursement 15 Physical network 48, 49 Physical product 21, 22, 24, 27, 28, 37, 40, 49, 51, 53, 54, 55, 57, 61, 62, 66 Physical supply of product 21 Populations change 12 Positive feedback 49 Potential annual production 15 Preservation 9 Prior analysis 140 Process optimization 53 Product development 34, 56, 60 Production function 24 Production planning 34 Projection system 34 Purchasing-production-marketing

Correlation and Regression Analysis: Applications for Industrial Organizations

196

81

R Raw material 39, 54, 72, 81, 85, 104, 106 Reduce agency 42, 43, 44 Relationship management 29 Representation state-space dynamic 188

S Scientific advancement 144 Social environment 8 Software market 48 Software product 45, 64, 67 Solid financial structure 9

Strategic framework 8 Subsequent application 10 Superior technology 68 Supplier-consumer relationship 32

T Technological innovations 9 Traditional market 66 Transaction cost 38 Transmitting information 43

V Versions generation 58 Virtual networks 49, 50

W Wealth generation 7