MLPS_08 09 Sixto Lopez Report

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Evaluating and implementing a forecasting model to estimate the

Aluminum Prices in CVG VenalumBy

Sixto A Lopez D

Report Submitted in Partial Fulfillment for a Master of Science degree inManagement of Logistics and Production Systems (MLPS) at the Ecole des Mines de

Nantes, France

Company Tutor

Luis M Salazar

Planning and Budget Manager

CVG Venalum, Av. Fuerzas Armadas

Puerto Ordaz Venezuela

School Tutor

Chams Lahlou

Lecturer, Ecole des Mines de Nantes,

4 rue Alfred Kastler, BP 20722, 44307

Nantes, France

INDUSTRIAL INTERNSHIP FINAL REPORT

January 2010


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Sixto A Lopez D Industr ial Internship Final Report

2 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.CONFIDENTIAL Privileged Information CVG Venalum proprietary information.

INDEX NOTE

Report title: An approach to reduce the error in the Prices forecast in CVGVenalum

Placement title: Industrial Project

Year: 2009

Author : Sixto Alexander Lopez Diaz

Company: CVG VENALUM C.A.

Address: Av Fuerzas Armadas, Edificio Corporativo Zona Industrial Matanzas, PuertoOrdaz, Estado Bolvar, Venezuela

Number of employees 3.700

Company Tutor: Mr. Luis Salazar

Role: Planning and Budget Manager

School tutor: Chams Lahlou

Key words: Industrial project, forecast, time series, Aluminium prices, budget

Summary: Along these years, the company (CVG Venalum)has been forced to go through

expensive revisions on the annual budget plans, partially due to the notablediscrepancies founded between the estimation of the aluminum prices and thereal performance of the market along the year in study.

Until now the sources of aluminum price forecast had been the ones offered bythe external information providers (exclusively by subscriptions), amongst themthe most important is CRU, a London based company which provides a vastseries of reports of pricing and market data, forecasts and market analysis andalso news and costs, however over the last four year, partially due to the highvolatility of the metals sector has placed substantial differences between theestimations and the real market prices provoking a negative impact in thecompany budget execution. Similarly, it has always been argued at managementlevel the need of having our own sources of aluminum prices estimations, whichin combination of the external providers can definitely improve the forecasting

precision and therefore reducing or eliminating midyear budget modifications orreformulations.So, given that aluminium prices tend to have a significant degree of impact onthe financial performance of the Company, coupled with the dominance of pricevariability over other factors that lead to variable revenues over time at anoperating smelter, the prime focus of this report is to analyze the ability of a timeseries forecasting model to predict future aluminium prices.


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3 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.

Acknowledgement

I give thanks to God for His mercies,

In memory of my beloved Grandmother, Eloisa, she will always be in my thoughts and prayers.

Thanks to my company CVG Venalum for giving me the opportunity to do this Master abroad and

additionally

Thanks to The Venezuelan Government Institution Gran Mariscal de Ayacucho for the scholarship

I would like to thanks to my industrial tutor Mr. Luis Salazar for his support, besides I want to

acknowledge my academic tutor Dr. Chams Lahlou from Ecole des Mines de Nantes for his guidance

and encouragement during the period of the Industrial project and the Master itself, also I would like to

express my gratitude to the Heads of the MLPS Program, Dr. Naly Rakoto and Prof. Pierre Djax for

their support and encouragement.

Sixto Lopez(Student Intern)

CONFIDENTIAL Privileged Information CVG Venalum proprietary information.


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TableofContentsContents

Acknowledgement 3

Table of Contents 4

1.0 Introduction 6

1.1 Host Company: CVG Venalum C.A. Aluminium Smelter 8

1.2 The Budget Department 8

1.2.1 Functional description of the CVG Venalum Budget Department. 9

1.2.2 Characterization of the Budget Department 9

1.2.3 CVG Vena lum Budg eta ry Proc ess 10

1.2.4 Budg et ing M od i fica t ion 11

2.0 Industrial Project Development 11

2.1. The Problem Statement 122.1.1. Project Objectives 14

2.2 Commodities, the London Metal Exchange and price discovery 153.0 Price forecasting 21

3.1 Price forecasting methods 22

3.2 The model: ARIMA (Autoregressive Integrated Moving Average) 25

4.0 The methodology: The Box Jenkins method for ARIMA processes. 26

4.1. Time series analysis of Aluminium prices 27

4.1.1 Te st fo r Sta tio na ry (First ste p ) 284.1.1.1 Removing non-stationarity in a time series 29

4.1.2 Id ent i f ic a t ion of the m od el , d ete rm in ing tenta t ive va lues of p , d , q . (Sec ond step ) 31

4.1.3 Estima tion of the ARIMA m o d el p a ra m et ers (Third ste p ) 36

4.1.4 Dia g no stic c he c king (Fou rth ste p ) 36

4.1.5 Fo rec a sting (Fifth ste p ) 37



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4.2 Results of the time series modeling using Statgraphics (output): 42

4.3 Comparisons w ith other models to check performance using Statgraphics 45

4.4. Comparison w ith the forecast o f the CRU GROUP Quarterly Aluminium Market Report 46

5.0 Savings 47

Conclusions 48

References 50



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1.0 Introduction

Budgets are business plans that are stated in quantitative terms and are usually based on estimations.

These plans aid an organization in the successful execution of strategies. Due to the uncertainties in

the business environment and / or due to wrong estimation, there may be significant deviations

between the actual and the plans. Budgets are useful in resource allocation whereby resources are

allocated in such a way that the processes which are expected to give the highest returns are given

priority. Index, in the early stage of the yearly budget formulation process of CVG Venalum some

specific premises are required and one of the premises is the estimation of the Aluminium price, CVG

Venalumas a State Company receives specifics guidelines from the government bureau Venezuelan

Corporation of Guayana or CVG some of these guidelines are the following:

National Inflation Rate

The Value Add Tax or VAT

The value of the government Tax

And the Bolivar/dollar exchange rate

LME Aluminium Cash price

All these guidelines come from Central Government, there is only one which is determined by the

industry, this premise is the Aluminium price, because of that at the mid of every year all the companies

which conform the Aluminium Group (two smelters, one alumina refinery and one anode facility) send

their planning analysts to have a series of meetings at the CVG Headquarters to establish by

consensus the Aluminium price that will be used as a premise in formulating the next year preliminary

budget of every plant.


In these meetings all the facilities analyst have to propose their respective price estimations based on

their own studies and above all in the information provides by independent consulting companies

focused on mining and metals, like CRU Group and Metal Bulletin Research (MBR). These meetings

are very important because the Aluminium price obtained there will be used as one of the premises to

calculate a preliminary budget for each individual facility. For this reason is compulsory to be as

accurate as possible, because if producer prices rise, assuming production levels and costs remain the

same, profits are expected to increase and all the contrary if there is a price decrease, but even more

important less deviations allows better resource allocation whereby resources are allocated in such a

way that the processes which are expected to give the highest returns are given priority.


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This is why Aluminium price estimation certainty is that important because once the Sales Plan of

Marketing is obtained with the Aluminium price we can calculate the profits of the company for the

forecasted period. Of course, the other premises are important as well, and they can also cause budget

midyear changes but only variations in price can provoke huge deviations in the amount of money that

enters into the company. Aluminium prices are central to the company investment decision and have a

significant impact on the financial performance of Aluminium National industry. Eggert (1987) provides

two reasons why Aluminium prices influence changes in a smelter cost structure. Firstly, present and

past price movements shape expectations about future prices and profits. Secondly, prices influence

smelting revenues and the cost of capital for financing expansions or future negotiations. From this

viewpoint, it would be particularly helpful if CVG Venalum could, by some means, forecast aluminium

prices to assist in their forward planning.

Unfortunately, in the last 4 years the CVG Venalum annual budget has suffered modifications in the

respective years due to the discrepancies between the forecasted prices and the real prices because

sometimes estimations have resulted to be too high or too low with respect to the real value, so If the

actual numbers delivered through the financial year turn out to be close to the budget, this will

demonstrate that the company understands their business and has been successfully driving it in the

direction they had planned. On the other hand, if the actuals diverge wildly from the budget, this sends

out an 'out of control' signal and the share price could suffer as a result.

The key research focus of the current report is the time series analysis of aluminium prices. The time

series technique of forecasting cash prices using ARIMA model is explored. A brief comparison of this

powerful forecasting method with others 4 methods is also provided.



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1.1 Host Company: CVG Venalum C.A. Aluminium Smelter

CVG Venalum was constituted in 1973 with the objective of producing primary aluminum in different

shapes for exporting purposes. CVG Venalum is a mixed capital company with 80% Venezuelan

capital, represented by Corporacin Venezolana de Guayana (CVG); and 20% foreign capital

according to agreement subscribed with a Japanese consortium integrated by SHOWA DENKO, K.K.;

KOBE STEEL, LTD.; SUMITOMO COMPANY, LTD.; MITSUBISHI ALUMINUM COMPANY, LTD.; and

MARUBENI CORPORATION, INC. Inaugurated officially on June 10th, 1978; C.V.G. VENALUM is the

largest Latin American aluminum smelter with an installed capacity of 430.000 tons/year. CVG Venalum

is located in Ciudad Guayana, Bolivar State on the southern margin of the Orinoco River. Seventy five

percent of its production is shipped to the United States, Europe, and Japan; the rest serves the

domestic market. CVG Venalums mission is to produce and commercialize products and services for

the aluminum industry in an efficient way as well as promote the development and strength of the

national aluminum industry downstream, maximizing the benefits for its workers, shareholders, the

region, and the country.

1.2 The Budget Department

The Budget Department is responsible for the review and preparation of the annual operating budget,

expenditure and revenue forecasts, rate and fee analysis, overall financial analysis regarding budgetary

matters, and budget development. The Budget Department supports all departments and divisions

within the Company as they prepare the next year's budget based on: prior year's expenditures; project

and investments, efficiencies and cost savings to be integrated from previous operating experience;

changes in mission, scope or sales plan; anticipated changes in available funding levels. The Budget

Department is a Division of the Budget and Planning Management, its principal mission is to compile

the annual company budget as a financial plan for the new financial year.



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1.2.1 Functional descript ion of the CVG Venalum Budget Department.According to the Functional Regulations and Norms of the Company, the Budget Department must

carry out the following main activities:

- To design and apply a correct application of the company budgetary system and assure

upgradeability and suitability

- To propose to the Chairman and Board of Directors the Budgetary Policy to apply in the budget

formulation according to the guidelines of the National Bureau of Budget issued through the

Venezuelan Corporation of Guayana (CVG).

- To guarantee the Budget formulation by management unit and the respective issue of the

Annual Company Budget, ensuring adequate prevision of budgetary supplies and resources

required by the company.

- To guarantee compatibility between the Annual Budget and the Company Plans and Objectives

- To guarantee that the modification process realized over the original budget are carried out

according to law and regulations

- To assist and support the others units in the budgetary formulation process and respective

control.

- To guarantee information availability for the Management Control Process

- To establish norms and rules programs to evaluate the budgetary system functioning with the

aim of detecting deviations and propose modifications to the Company Direction in order to

accomplish the objectives.

- To carry out studies and analysis of the variables that could affect the budgetary management

in order to make estimations of the financial resources required.

- Gathering of information for the budget formulation, budget modifications and budgetary

sceneries elaboration.

- To evaluate budgetary transfer issues in order to determine suitability and legality

- To guarantee the timely issues of reports for Government and main headquarter offices uses.

1.2.2 Characterization of the Budget Department


As a matter of practice, the entire budgeting process in CVG Venalum is shown in the diagram 1

below, we can observe all the components that integrate the CVG Venalum Budget Formulation:


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Diagram 1

Suppliers

MIBAMPlanning and FinanceBureauPlanning andDevelopment BureauNational Bureau ofBudgetNational AuditDepartmentNational Commission ofCurrency Administration

Venezuelan CentralBankVenezuelan Corporationof GuayanaBanks and InvestmentInstitutionsLogistics ManagementLaw DepartmentFinance andAdministrationManagementPersonnel DepartmentIndustrial EngineeringDepartmentProject DepartmentAll the Company Units

Input

Guidelines of the NationalBureau of BudgetGuidelines from Governmentand Independent OfficesGuidelines from the CompanyBoard of DirectorsStatements from the VenezuelanCorporation of GuayanaFinance Government PoliticsSalary Government StatementsCompany warehouse Inventory

GuidelinesCompany Strategic PlansExpansion Projects StatusCash Flow projectionCurrencies requirementsMacro-economics indicatorsCompany Production PlanSales Plan and Sales ConditionsInvestment Plan and ServiceProvidersRaw material prices andmaintenance servicesExpenditure PlanServicesPurchasing PlanConsumption FactorsConsumption programs of rawmaterials

Process

To identify budget needsrequested for the planoperations in the short, mediumand long termApproved Investment ProjectsRequirements EvaluationTo evaluate requirementsaccording to the ApprovedStrategic PlanBylaw, regulations and statutesTo analyze projected financial

statementsTo analyze project cash flowTo evaluate and guide budgettransfers of budgetaryappropriationExecution and controlTo establish and executepreventive and correctiveactions

Products

Approved fiscal annual budget

Budgets modifications

Budget by Project

Clients

MIBAMPlanning and Finance BureauPlanning and DevelopmentBureauNational Budget Department(ONAPRE)National Audit DepartmentCVGCVG Venalum Board ofDirectorsPresidency

All Company Units(Management)Congress Commission forFinance Administration

Att ributes

Opportuneness Reliableness Availability Objectiveness

Resources

Personnel Budgeting System Computers Budget Assignation

At tr ibutes

Efficiency Effectiveness Opportuneness Assertiveness Credibility

Di

1.2.3 CVG Venalum Budgetary Process

All department managers within CVG Venalum must accurately determine their future costs and must

plan activities to accomplish corporate objectives. Departmental supervisors must have a significant

input into budgeting costs and revenues because these people are directly involved with the activity

and have the best knowledge of it. Managers must examine whether their budgetary assumptions and

estimates are reasonable. Budget targets should match manager responsibilities. At the departmental

level, the budget considers the expected work output and translates it into estimated future costs. For


Venezuelan Republic Constitution - Finance Administration Law of the Public Sector Annual Budget Law Venezuelan Audit Law Company Regulatory Statements Board ofrectors Resolutions CVG and MIBAM Guidelines Budget Modifications Procedures and Rules Anti-Corruption Regulations ISO 9000 norm Development and Social National Plan

REGULATORY SCHEME


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each department the Budget Department collects information and data. The sales department must

forecast future sales volume of each product or service as well as the Aluminium selling price. It will

also budget costs such as wages, promotion and entertainment, and travel. The production department

must estimate future costs to produce the product or service and the cost per unit. The production

manager may have to budget work during the manufacturing activity so the work flow continues

smoothly. The purchasing department will budget units and dollar purchases. There may be a

breakdown by supplier. There will be a cost budget for salaries, supplies, rent, and so on. The stores

department will budget its costs for holding inventory. There may be a breakdown of products into

categories. The finance department must estimate how much money will be received and where it will

be spent to determine cash adequacy.

1.2.4 Budgeting Modi fication

CVG Venalumbudget is monitored regularly. The company budget is periodically revised to make it

accurate during the period because of error, feedback, new data, changing conditions (e.g., economic,

political, corporate), or modification of the companys plan. A change in conditions typically will affect

the sales forecast and resulting cost estimates. We have to keep in mind that revisions are more

common in volatile industries like the commodities sector. The budget revision applies to the remainder

of the accounting period. A company may roll a budget, which is continuous budgeting for an

additional incremental period at the end of the reporting period. The new period is added to the

remaining periods to form the new budget. Continuous budgets reinforce constant planning, consider

past information, and take into account emerging conditions. The problem is that when a budget

modification is required, all the whole process must be done again to apply the respective corrections,

wasting company resources and time. The annual budget is revised when errors are found or

circumstances change. Revisions would be required for changes in cost estimates, unexpected

developments in the economy, design changes, technological developments, action by competitors,

change in divisional or departmental objectives, and casualty losses.


2.0 Industr ial Project Development


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2.1. The Problem Statement

The company has identified from recent audits that the budge company has been revised every year

over the last 4 years and one the main causes of the revisions has been the substantial variations

between the aluminum price forecast and the price real performance. Therefore, this report analyses

the ability of a user-friendly time series forecasting techniques to predict future Aluminium prices. The

conclusion is that price forecasting is difficult. It should, however, be acknowledged that whilst any

model is perfect, they are useful for the Budget company planning process. In particular, the results

from the analysis in this paper suggest that ARIMA modeling provides marginally better forecast results

than others price modeling. The methodologies employed in this report have a broad based application

to base metal forecasting by smelter and refineries in general, that is, the applications are transferable.

In table 1below are shown the estimations of Aluminium prices ($/t) for the Approved budget with its

respective modifications since the year 2004:

Table 1: Aluminium price budget estimations vs real prices $/ t (2004 - 2010)

Ao First Estimation Second Estimation Real LME Cash Variation (abs)

2004 1579 1715 1716 137

2005 1580 1816 1899 319

2006 1776 2100 2569 793

2007 2100 2650 2588 488

2008 2500 2700 2572 72

2009 2750 1415 1668 10822010 1500 1650 2200* 700

Average variation 513

*2010 forecast

Source: CVG Venal um Budget Department Services 2009

Over the years is observed that the Aluminium price has been recalculated due to the significant

differences between the approved price used and the real tendency of the price along the year.

This recalculation implies that more money have to be expended in overtime working hours to

reformulate the budget but also in meetings to obtain the new approval for the Board of Directors, but

above all, modifications imply expensive delays in projects and investments that could have been

carried out on time or not carried out at all.


The quantification of the costs that imply annual Budget modifications will be seen with some detail

later on this paper, bearing the above in mind, the prime aim of this report is to analyze one time series

forecasting method in terms of their ability to forecast aluminium prices. The methodological


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approaches are tested using London Metal Exchange (LME) cash for aluminium over the period

firs t quarter 1985 four th quarter 2009.

One important factor that must be determined is what will it be the acceptable error in a forecast to

avoid a budget modification? Well, based on historical data we could established the error limit as

follows in table 2

HISTORICAL MAD VALUES OVER 300$/t

WORD REFERENCE AVERAGE VALUES 300 $/t

DEVIATION 100 $/t

MAD TARGET (QUARTELY) 200$/t

Source: Company Budget Department estimations

The Mean Absolute Deviation in the aluminium price has been expected to be over 300 $/t, it has been

estimated that values equal or lower than 200 $/t could make the forecast acceptable and it would not

be necessary to carry out any budget modification.

On the other hand, the price information providers costs of CVG Venalumare detailed in the table 3

below:

Table 3

Consulting firm Subscription Annual Costs

CRU Aluminium Quarterly report 10.000 Pounds/year

James F King Quarterly Report 2.000 $/year



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2.1.1. Project Objectives

As previously mentioned, the main objective of the project is: to analyze the ability of a time series

forecasting model to predict future aluminium prices in order to avoid costly budgetary modifications

due to this factor.

Specific objectives: these include:

Analyzed budget years handbooks with the aim of determine the budgeting price for each year

from 2004 to 2008 and the corresponding price modification for each respective year.

Studied and determined of the price difference between the Budget Department forecast,

estimated through the consensus of all the aluminum holding (the aluminum holding is

composed by two aluminum smelters, one main aluminum final product fabricator, one hydro-

electricity company and one alumina refinery), the external information provider and the real

market price over the last 4 years.

To obtain the historical data of the quarterly LME aluminum prices from 1985 to date.

To evaluate what has been the impact of the aluminum price forecast in the budget estimation

along the last 5 years

To find out how the aluminum is traded on an exchange, specifically the LME. Examining the

fundamentals of commodities and commodity trading in general, followed by an overview of

metal trading specifically on the LME, because only when the issues surrounding the price

formation process for aluminum are fully understood can forecasting strategies be put into

context(Dooley, 2005)

Determine the proper time series model that fit the most to the aluminum price behavior based

on the characteristics of the history observations and on the context in which the forecasts are

required.


Identify the appropriate ARIMA model for a time series, beginning by identifying the order(s) of

differencing needing to stationarize the series and remove the gross features of seasonality,

perhaps in conjunction with a variance-stabilizing transformation such as logging or deflating.

Once the results of the research are reached, to prepare the final report and to make the

appropriated conclusions and recommendations


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Once the model is chosen, forecast method of monitoring must be implementing to have regular

supervision of the results and to see if the model is appropriate or if some unforeseen change

has occurred in the series.

2.2 Commodities, the London Metal Exchange and price discoveryBase metals such as Aluminium are traded on an exchange, specifically the LME. Therefore, it is

appropriate at this point to firstly examine the fundamentals of commodities and commodity trading in

general, followed by an overview of metal trading specifically on the LME. Only when the issues

surrounding the price formation process for aluminum are fully understood can forecasting strategies be

put into context.

2.2.1 Commodity Exchange TradingCommodities are generally categorized as metals, soft, energy and grains, to name but a few. These

are traded on a commodity exchange, which is essentially a market for the sale or purchase of

commodities for immediate delivery and delivery in the future. Metal contracts and the exchanges on

which they are traded are presented in table 4. The volume of minerals actually traded on the

commodity exchanges is relatively small and the published transaction prices form the basis for pricing

most similar material throughout the world. A very small percentage of trading results in the delivery ofthe underlying commodity. The vast majority of contracts are closed out before they expire by an

offsetting futures trade. Essentially, physical commodities normally change hands on a local level on

what is known as the cash market or local market where actual commodities are bought and sold. It

reflects local supply and demand. However, futures contracts on these commodities trade on futures

exchanges, reflecting world supply and demand. It is thus on the basis of the prices established on the

exchange floor that cash market prices are decided.



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Table 4

Major metal exchanges of the World

London Metal Exchange (LME)

Exchange/metals trade Future delivery Options delivery Units

Copper To 63 months To 63 months US$/t

Aluminium To 63 months To 63 months US$/t

Aluminium To 27 months To 27 months US$/t

Alloy

Nickel To 27 months To 27 months US$/t

Lead To 15 months To 15 months US$/tZinc To 27 months To 27 months US$/t

NASAAC To 27 months To 27 months US$/t

Tin To 15 months To 15 months US$/t

New York mercantile exchange (NYMEX Division)

Platinum To 15 months To 11 months US$ and /troy ounce

Palladium To 15 months Not traded US$ and /troy ounce

New York mercantile exchange (COMEX Division)

Copper To 23 months To 22 months US/pound

Gold To 60 months To 24 months US$ and /troy ounce

Silver To 60 months To 24 months US/troy ounce

Aluminium To 25 months To 21 months US/pound

Tokyo commodity exchange (TOCOM)

Gold To 12 months To 8 months

(call & put)

/gram

Silver To 12 months Not traded 0.1/10 grams

Platinum To 12 months Not traded /gram

Aluminium To 12 months Not traded 0.1/kilogram

Sources: London Metal Exchange (2005), Tokyo Commodit y Exchange (2005); New York Mercantile Exchange (2005)


All exchange-traded commodities are quoted in standard terms. For example, the Aluminium contract

specification is shown in Table 5. The commodities traded must comply with a standard specification


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for quality, weight and shape in order that they will be accepted by a large number of sellers and

buyers. This allows for ease of transfer and thus adds liquidity to the market.

Table 5: Aluminium Specification

LME Aluminium Futures Contract Specification

Contract: Aluminium of 99.7% purity (minimum)

Lot size: 25 tonnes (with a tolerance of +/- 2%)

Form: 1. Ingots2. T Bars3. Sows

Weight:

1. 12 26 kg each. Parcels of ingots on warrant shall not exceed 2 tonnes each2. Shall not exceed 5% more than 750 kg

3. Shall not exceed 5% more than 750 kg

Delivery dates:

Daily from cash to 3 months (first prompt date two working days from cash). Thenevery Wednesday from 3 months to 6 months. Then every third Wednesday from 7months out to 63 months

Quotation:

US dollars per t

Minimum PriceMovement:

50 US cents per t

Clearablecurrencies:

US dollar; Japanese yen; sterling; euro

LME Aluminium Options Contract Specification

Delivery dates:

Monthly from the first month out to 63 months

Value date: The third Wednesday of the prompt month

Exercise date: The first Wednesday of the prompt month

Premium quotation: US dollars per t

*Strike price:

$25 gradations for strikes from US$25 to US$1975$50 gradations for strikes from US$2000 to US$4950$100 gradations for strikes over US$5000

*Strike price gradations and tick size for premiums available in all clearable currencies.



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2.2.2 Exchange participantsExchange participants can be distinguished in terms of their motives for trading. The two major

categories are hedgers and speculators. Hedgers wish to minimize price risk while speculators aim to

make a profit from the very risk that hedgers wish to avoid. Given that the number of buyers and sellers

of contracts is never the same, the key purpose of exchange speculators is to provide liquidity in the

market, so that for every buyer there is a seller and for every seller there is a buyer.

The leveraged nature of derivative contracts makes them particularly attractive investment vehicles for

skilled speculators. This means that, for a small down payment, large gains can be made. While the

LME is still very much a trade-driven market (implying that the commodity price in a commercial market

is driven by the interaction of buyers and sellers) rather than a speculator-driven market (implying that

speculators have not really been active in the base metals commodity market), investment activity

accounts for about 20% of turnover (Tudor, 1997)

Hedgers, on the other hand, use the market as a means of risk management. Conceptually, mining

companies can be regarded as the suppliers of metal to end users, with smelters charging a fee for

transforming the concentrate into user form. Thus, commodity prices are of direct concern to them.

Depending on the price of the metal (determined by various forces on the exchange which are

discussed in this report), the sale price to smelters and thus the revenue received from the concentrate

sale fluctuates. Yet the net return they receive still depends on the international commodity price. In this

light, they can trade the underlying commodity on the cash market but trade futures contracts in a

central marketplace such as the LME to reduce the effects of adverse price movements.

2.2.3 Metal trading on the London Metal Exchange

The LME is one of the worlds longest established futures exchanges, incorporated in the 1870s as a

trade forum for metal merchants and dealers. Over the years it has progressed to become the most

successful non-oil commodity exchange in the world, trading in copper grade A, primary Aluminium,

standard lead, primary nickel, tin, special high grade zinc, Aluminium alloy and North American SpecialAluminium Alloy (NASAAC) (London Metal Exchange, 2005).

The three key functions of the LME are summarized as follows:


Price discovery: Providing reference prices which are accepted globally and widely used in the

non-ferrous metals industries for benchmarking. (http://www.lme.co.uk/pricing.asp)


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Hedging, this is the reason for commodity exchanges: Providing a market where participants,

primarily from non-ferrous base metals related industries, have the opportunity to protect against

risks arising from movements in base metals prices. (http://www.lme.co.uk/risk.asp)

Delivery: Providing for appropriately located storage facilities to enable market participants to

make or take physical delivery of approved brands of LME traded metals.

(http://www.lme.co.uk/warehousing.asp)

The first key function above, price discovery, involves the determination of a uniform and representative

price level to facilitate transactions (Radetzki, 1990). It is here that buyers and sellers meet

simultaneously and these underlying supply and demand forces come together to determine prices.

The prices at the exchanges are instantaneously influenced by events taking place in the outside world.

The daily price quotations for cash, 3-month, 15 - month and, where applicable, 27-month contracts

established on the exchange must be efficiently registered, monitored and disseminated to everyone

involved in the metal trade. The second key function, hedging, is a means of metal price risk

management. Hedging is undertaken to protect against downward price swings, whereby the value of a

derivative contract moves in the opposite direction to the commoditys price change, thus negating the

effects of downward price movements. Warehousing/delivery is another important function of the LME;

after all, real commodities are being exchanged and need to be stored appropriately, which is different

to a financial exchange for instance, where financial instruments are traded. Given the price forecasting

focus of the current report, the price discovery process is now examined in detail to set the scene for

the metal price forecasting discussions and analysis that follows.

2.2.4 Price discovery


There are several important reasons for studying the price discovery process. Of all the factors that

lead to variable revenues over time at an operating smelter, the greatest source of variability has

generally been found to be metal price (although at an Aluminum smelter, there are likely to be other

sources of risk, such as technical risk associated with smelting technology, reliable electricity and

mineral sources, that may be just as important). According to a study by Borensztein et al. (1994),

commodity prices are characterized by trends, cycles and increasing volatility. For example, Fig. 1

illustrates the high volatility of metals prices compared with financial currencies (Tudor, 1997: 54).This

could be attributable to some of the unique characteristics of the market for metals. For instance, in


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terms of supply and demand, the demand for metals is generally more volatile than financial currencies,

due possibly to the strong link between metal demand and the macroeconomic business cycle. The

more attractive government policy is towards the smelting industry (which is in the business of making a

profit, not producing metals), the higher the likelihood that the supply of metals will increase. A further

reason is that metals are price inelastic and subject to large shifts in demand over the business cycle

while production capacity changes very slowly. Yet not all studies have found volatility to increase over

time. Brunetti and Gilbert (1995)in a study that used a complete record of daily price quotations from

LME over the period 19721995 for the six LME metalsso as to construct a set of monthly volatility

measures, found volatility showed no tendency to increase over the period. Either way, it should be

acknowledged that a low level of volatility does not imply low price variability and it would be useful for

aluminium producers if they could forecast variances in price over time.

Gocht et al . (1988)describe how price formation can occur in four ways: either on an exchange by the

forces of supply and demand, by regulation via international cartel or commodity agreement, by

negotiation between producers and consumers or, finally, prices can be fixed by monopolistic or

oligopolistic producers. The determination of which of the above forms price takes depends on various

factors ranging from the degree of competitiveness in the market to the existence or otherwise of cartel

agreements and other price controls. Kernot (1991) emphasizes how base metal price forecasting is

much more tied to supply and demand, with less contribution from investment demand (which contrasts

with the holding of precious metals by investors as a measure of value).

Fig. 1

Volatility %

0 5 10 15 20 25 30

Dollar/DM

Zinc

Tin

Lead

Copper


Source: Tudor (1997: 54)


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Non-market price formation methods either (a) signal a certain amount of market power in the hands of

the participants or (b) are used by convention. Above all, however, it should be borne in mind that,

given that they all attempt to outwit the market, they could be considered as a distortion. The LME

price, determined by the largely unimpeded forces of supply and demand, is the most transparent price

mechanism and this justifies an analysis of hedging and forecasting of market determined prices. It

would, however, be naive not to acknowledge the fact that, whilst it is certainly true that LME prices are

transparent and that most if not all LME contracts represent (nearly) perfectly competitive markets, this

cannot be interpreted as saying that the presence of commodity trading for a commodity implies perfect

competition, as this is not necessarily the case. Commodity exchange trading requires a large number

of buyers and sellers. It is possible that one or more buyers or sellers is/are large enough to influence

price; and also as the scale of investment in commodity markets has grown, speculation has emerged a

factor in its own right, a new "fundamental" alongside traditional physical supply and demand. It raises

the difficult question of what happens if the weight of investment money moves prices away from their

fundamentally determined equilibrium value for a prolonged period? Most analysts insist this is not

possible. But the widely acknowledged housing bubble and mispricing of risk in credit markets have

shown markets can deviate from fundamental valuations for years at a time. If credit and housing

markets can misprice assets, there is no reason commodity markets should be any more "accurate"

(John Kemp 2009).

While hedging is an ongoing, real-time means of price risk management, price forecasting is necessary

for price risk management into the future and both strategies are intrinsically linked. No forecast will

ever be fully accurate, thus the need to hedge against price movements. Hedging strategies are formed

based on a view of what price might be in the future and this is where price forecasting models come

into play, in terms of informing hedging strategies. The sole focus of this paper hereafter is with respect

to price forecasting strategies.

3.0 Price forecasting


Price forecasting is important to investigate things as primordial as whether a Smelter Greenfield

Project can be developed or not or if some ongoing internal investment projects might be cancelled or

delayed but also no so important like salaries rises or bonus emissions. The production decision-

making process involves examining both potential revenues and costs, with price central to revenue


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generation possibilities. Forecasting involves choosing the duration to be examined, choosing an

appropriate technique or techniques, gathering the data to be analyzed and testing the model. While

the forecasting of production and technology are relatively straightforward, price forecasting is much

more complicated and much research effort has been devoted to this topic.Long-term forecasts are

more unreliable than short-term ones and it should be remembered that no forecasting methodology

will be fully accurate all of the time so there are risks associated with using them. As Van Rensburg

(1978)points out, forecasting remains an art rather than a science.

3.1 Price forecasting methods

A company may choose from a wide range of forecasting techniques. There are basically twoapproaches to forecasting, qualitative and quantitative:

1. Qualitative approachforecasts based on judgment and opinion Executive opinions

Delphi technique

Sales force polling

Consumer surveys

2. Quantitative approach

a. Forecasts based on h istor ical data

Naive methods

Moving average

Exponential smoothing

Trend analysis

Decomposition of time series

b. Associative (causal) forecasts

Simple regressionMultiple regression

Econometric modeling


In terms of trend extrapolation and time-series methods, which are of direct relevance to this report,

they attempt to forecast by extrapolating from past trends of prices. In other words, they empirically


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evaluate trends. Time-series methods are superior to trend extrapolation in their rigor and

sophistication. Figure 1 summarizes the forecasting methods. The list presented in the exhibit is

neither comprehensive nor exhaustive, but Table 6 below shows the inherent strengths and

weaknesses of both methods.

Figure 1: Forecasting methods classification

FORECASTING

QUANTITATIVE(STATISTICAL)

MARKOVANALYSIS

QUALITATIVE(Judgmental)

INDIRECT

LEARNEDBEHAVIOUR

Barometric Input/Output Market Surveys

ExpertOpinion

Sales forcepolling

Co ns umer Sur veys Delp hi m eth odCAUSAL

(REGRESION)TIME SERIES

Simple

Multiple

Econometric MovingAverage

ExponentialSmoothing

ClassicalDecomposition

Box-Jenkins

Figure 2: source Budgeting basics & Beyond Page 227



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Table 6 Trend and Time Series forecasting

Method Description Strengths WeaknessesTrendextrapolation

Empirical evaluation of trends Simplicity

Limited datarequired

Low cost

Lack of structural content

Lack of response tochanges in externalfactors

Inability to recognizebusiness cyclefluctuations

Lack of statisticalinference

Not good for long term

forecasting

Time-Series The past behavior is examined in order toevaluate possible trends. For example, ifGDP grew at 4% for the last 20 years itwould be expected to continue to grow at 4%the following year. These models mayrequire some simple extrapolation method,such as linear trend model or more.

Knowledge ofrelationships andeconomics notneeded

Short-termforecast accuracysimple

No causal relationship

Assumes consistency inchange and uniformity ineffect in change

Box-Jenkins The Box-Jenkins or auto-regressive moving-average model (ARIMA) gives thedependent variable as a function of lagged

random disturbances terms, in order to usean algebraic equation with fixed coefficientsthat can be estimated on the basis of pastdata

Accounts forhistorical changes

Non-linear patterns

are manageable

Costly to produce

Large amount of timerequired

Deciding on laggedaffects entails a great dealof subjectivity.

Source: (Makridakis 1998): Forecasting Methods and Applications

An in-depth discussion of the costs and benefits associated with employing each of the methods above

is most definitely merited in terms of moving the debate forward. Such a focus on all forecastingmethods, however, is beyond the remit of the present report, which concerns itself specifically in using

a time series method in aluminium price forecasting.



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because the stationary ARMA model to the differenced data has to be summed or integrated to

provide a model for the nonstationary data, it is just a combination of the autoregressive (AR) and the

moving average (MA) models, so in general, in an ARMA ( p, q) process, there will be p

autoregressive and q moving average terms, but as we have to difference a time series d times to

make it stationary and then apply the ARMA(p, q) model to it, we say that the original time series is

ARIMA(p, d, q), that is, it is an autoregressive integrated moving average time series, where pdenotes

the number of autoregressive terms, dthe number of times the series has to be differenced before it

becomes stationary, and qthe number of moving average terms. Thus, an ARIMA (2, 1, 2) time series

has to be differenced once (d = 1) before it becomes stationary and the (first-differenced) stationary

time series can be modeled as an ARMA(2, 2) process, that is, it has two AR and two MA terms.

Having explained this we will now apply the methodology to fit our time series data to the model. A

mixture ARIMA process (p, d, q), in our example case (2, 1, 2) would be written as follows:

=tY ++ 2211 tt YY +' 2211 ttt eee

AR(2) Process Constant MA(2) Process

Here Yt depends on two previous Yt-1 and Yt-2 values and also on two previous error terms 2211 tt ee ,

the series is assumed stationary in the mean and in the variance.

4.0 The methodology: The Box Jenkins method for ARIMA processes.


The emphasis of these methods is not on constructing single-equation or simultaneous-equation

models but on analyzing the probabilistic, or stochastic, properties of economic time series on their own

under the philosophy let the data speak for themselves. Unlike the regression models, in which Y t is

explained by k regressor X1, X2, X3. Xk, the BJ-type time series models allow Ytto be explained by

past, or lagged, values of Y itself and stochastic error terms. For this reason, ARIMA models are

sometimes called atheoretic models because they are not derived from any economic theory - and

economic theories are often the basis of simultaneous-equation models.The question obviously is:Looking at a time series, such as the aluminium LME Cash quarterly series in Figure 3, how does one

know whether it follows a purely AR process (and if so, what is the value of p) or a purely MA process

(and if so, what is the value of q) or anARMA process (and if so, what are the values of p and q) or an

ARIMA process, in which case we must know the values of p, d, and q. The BJ methodology comes in

handy in answering the preceding question. The method consists of five steps as shown in figure 2:


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Figure 2: The Box Jenkins methodology for ARIMA models

Differencing the series to achievestationarity

Identification of the model (choosingtentative values of p, d and q)

Parameters estimation of thetentative model

Diagnosticchecking, isthe tentative

modeladequate?

NO

Use the model for forecasting and

control

YES

1st step

2nd step

3rd step

4th step

5th step

4.1. Time series analysis of Aluminium prices


Aluminium price forecasting can be attempted using time series analysis, but application of any

forecasting methods involves two basics tasks: Analysis of the data series and selection of the

forecasting model that best fit the data series; in addition, according G.S Maddala (2002, p. 519) the

processes that better describe commodity and stock prices behavior are the random walk processes

(processes that assume a constant mean and a constant variance), we will use the ARIMA model

because this method uses the realization to draw inferences about the underlying stochastic process of

a time series, similar to how sample data is used to draw inferences about a population (Gujarati,

2004). The variables will be initially checked for stationarity following the Box Jenkins methodology.

The data used here are LME cash and 3 month prices in a quarterly basis for Aluminum from 1st

quarter 1985 to 4th quarter 2009. (See figure 3 below). Tables 7 and 8 contain the results of the

Dickey Fuller to check for stationarity which were obtained from Microfit (acronyms used are also


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stated in these tables).

Figure 3:

Quartely average LME Cash ($/T)

500

1, 250

2, 000

2, 750

3, 500

1985Q1

1987Q2

1989Q3

1991Q4

1994Q1

1996Q2

1998Q3

2000Q4

2003Q1

2005Q2

2007Q3

2009Q4

Quartely basis

AlCash

$/t

4.1.1 Test for Stationary (Firs t step)

Broadly speaking, a stochastic process is said to be stationary if its mean and variance are constant

over time and the value of the covariance between the two time periods depends only on the distance

or gap or lag between the two time periods and not the actual time at which the covariance is

computed (Gujarati, 2004, p. 797). In other words the mean, variance and auto-covariance (at various

lags) stay the same no matter what time they are measured. A test for stationarity is necessary

because the classical linear regression model requires that all variables are stationary. Regression

models detect correlations and if a regression is carried out on non-stationary variables, this could lead

to a spurious regression or spurious correlation, that is, the regression has a high R2and t-statistics

that seem significant but the results have no economic meaning.


To test for stationarity, the Dickey Fuller (DF) statistic is computed. This is compared to a critical

value at a 95% significance level. The unit root hypothesis states that a time series that has a unit root

is a random walk time series and is an example of a non-stationary time series. If the test statistic is

greater than the critical value, then the time series is stationary. Dickey and Fuller have shown that

under the null hypothesis that = 0, the estimated t value of the coefficient of Yt1 in (2.1.9.a)follows

the (tau) statistic. These authors have computed the critical values of the tau statistic on the basis of


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Monte Carlo simulations. A sample of these critical values is given in Appendix A, Table 11.

Using the LME Quartely price data for aluminium prices (PA) from 1stquarter 1985 to 4thquarter 2009,

the equation to be estimated is as follow:

ttt PAPA ++= 11 (2.1.9.a)

Where:

= Constant term

j = jth autoregressive parameter,

t = The error term at time t

In this case we use Microfit, (software for econometrics) which provides the ADF statistic and critical

values for each variable. The results of this test for stationarity are shown in Table 7. In this case, the

test statistic (DF statistic) is less than the critical value. Therefore, the null hypothesis that the prices

contain a unit root cannot be rejected. In other words the variables are non-stationary.

Table 7: Test for I(0) stationarit y

Variable Acronyms DF Test Statistic Critical DF (at 95%)

Aluminium cash price CASHPA 2.1327 3,45

4.1.1.1 Removing non-stationarity in a time series


Although most of time series models assume stationarity, one often encounters nonstationary time

series, the classic example of the random walk model (RMW) are the stocks and commodities prices, it

is important to remove the non-stationarity before proceeding with time series model building, this canbe achieved routinely through the method of Differencing, for instance, considering the prices quarterly

series 1089.63, 1081.23, 1005.33, 986.652002.65 consisting of a linear trend non randomness.

Subtracting consecutives values, 1081.23 - 1089.63, 986.65 1005.33 etc, gives at the first

differences, the absolute series 8.4, 75.90, 18.68, 147.38190.80 (see Appendix A: Table 12).

These series will be demonstrated in table 8with the application of the second Dickey fuller test to


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be clearly stationary, thus to achieve stationarity, a new series is created that consists of differences

between successive periods:

4.1.1.1b

If a time series is differenced once and then becomes stationary, the original (non-stationary) series is

integrated of order one, denoted by I (1). Then, a second ADF testis required using first differences.

The new equations to be estimated are the following:

ttt PAPA ++= 11 (4.1.1.1c)

The results of this test using Microfit for I(1) stationarity are shown in Table 8.

Table 8: Test for I(1) stationarit y

Variable Acronyms DF Test Statistic Critical DF (at 95%)

Aluminium cash price CASHPA 6,3346 3,45

This time the test statistics is quite greater than the critical value. Therefore, H0 (that DPA IS non-

stationary) is rejected. The variable DPA is stationary. The variable is also integrated of the same

order, that is, equal I(1). Once a series of variables has been made stationary and that they are

integrated of the same order, it is possible to examine the autocorrelations to see if any pattern remains

(that is, other than randomly scattered around zero), this method can be used just to confirm

stationarity:



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Block 1:Autocorrelations and the resulting correlograms from the first differenced aluminium prices dataobtained using Stat graphics

Lags

Au to-

correlation

1 0.24359

2 -0.03468

3 -0.16199

4 -0.05042

5 0.00536

6 -0.05814

7 -0.09503

8 -0.04257

9 0.16467

10 -0.07132

11 -0.13963

12 -0.11693

13 -0.07558

14 -0.01757

15 -0.00634

16 -0.02819

17 -0.01695

18 -0.01837

19 -0.06286

20 -0.01628

21 -0.02774

22 -0.07338

23 -0.0008624 -0.00681

First differenced Autocorrelations

4.1.2 Identification of the model, determining tentative values of p , d, q. (Second step)

The chief tools in identification are the autocorrelation function (ACF), the partial autocorrelation

function (PACF), and the resulting correlograms, which are simply the plots of ACFs and PACFs

against the lag length. Once we have used the differencing procedure to get a stationary time series,

we examine the partial correlograms to decide the appropriate orders of the AR and MA components.

The correlograms of a MA process is zero after a point, while the one of an AR process declines

geometrically. Now the correlograms of an ARMA process show different patterns (but all dampen after

a while). For the analysis of the ARIMA orders we have to introduce the concept of the Partial

Autocorrelation Coefficient (PACF). In regression analysis, if dependent variable Y is regressed on

independent variables X1 and X2 then it might be of interest to ask how much explanatory power does


The visual plot of the time series is enough to convince a forecaster that thedata is stationary, the autocorrelation of a stationary data drop to zero after thefirst time lag, while for a nonstationary series they are significantly differentfrom zero for several time periods (Makridakis, 1998, p. 379). The block 1

above shows the graph of autocorrelations for a stationary series after beingfirst differentiated.

0 5 10 15 20 25

-1

-0.6

-0.2

0.2

0.6

1


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X1 have if the effects of X2 are somehow partialled out first. Typically, this means regressing Y on X2,

getting the residual errors from this analysis and regressing the residuals against X1. In time series

analysis the concept is pretty similar; Partial Autocorrelations are used to measure the degree of

association between Yt and Yt-kwhen the effects of the other time lags 1,2,3, up to k-1 are somehow

been partialled out; their singular purpose in time series analysis is to help identify an appropriate

ARIMA modelfor forecasting, in fact, they have been constructed just for this use (Makridakis, pag.

372, 1998).

But how do we determinate the grade of the AR and MA terms?, before we have to state that

we will consider only the first di fferenced aluminium prices series because it is stationary. If the

underlying process generating a given series is anAR (2) model, in model identification , it is assumed

that if there are only two significant partial autocorrelations, the generating process is of second order

and the order of forecasting model should beAR (2). If there are p significant partial autocorrelations,

then the order should beAR (p). Then,for identification purposes, therefore if the process is an

autoregressive one its (ACFs) autocorrelations coefficients decline to zero exponentially and the

partials (PACF)correlations can be examined to determine the order of the process (Makridakis,

1998, page. 375). That order is equal to the number of significant partial autocorrelations.

Now if the generating process is MA rather than AR, the partial correlations will not indicate the order of

the MA process, since they are constructed to fit an AR process, Notice that the ACFs and PACFs of

AR (p) and MA (q) processes have opposite patterns; in the AR (p) case the AC declines geometrically

or exponentially but the cuts off after a certain number of lags, whereas the opposite happens to an MA

(q) process. For identification purposes, when the (PACF)partial autocorrelations do not exhibit a drop

to random value after p time lags but instead decline to zero exponentially, it can be assumed that the

true generating process is a MA one (Makridakis , 1998, page. 375). Geometrically, these patterns are

shown in Figure 4.



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Figure 4:ACF and PACF of selected stochastic processes: (a) AR(2): 1= 0.5, 2= 0.3; (b) MA(2):1= 0.5, 2= 0.3; (c) ARMA (1, 1): 1= 0.5, 1= 0.5. (Gujarati, 2004, page 845)



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Block 2: Autocorrelations (ACF) and the resulting correlograms from the LME Cash aluminium prices dataobtained by using Stat graphics module of forecasting

Lags

Au to -

correlation1 0.24359

2 -0.03468

3 -0.16199

4 -0.05042

5 0.00536

6 -0.05814

7 -0.09503

8 -0.04257

9 0.16467

10 -0.07132

11 -0.13963

12 -0.11693

13 -0.07558

14 -0.01757

15 -0.00634

16 -0.02819

17 -0.01695

18 -0.01837

19 -0.06286

20 -0.01628

21 -0.02774

22 -0.07338

23 -0.00086

24 -0.00681

Aut ocorrelations ACF f or 24 lags for fisrt di ff renced aluminium pr ices series

The visual plot of the aluminium prices time series ACF is quite enough toconvince a forecaster that the autocorrelations coefficients decline to zeroexponentially (NOT SLOWLY) after the first time lags, behavior that is veryparticular for AR processes, therefore the partial autocorrelations can beexamined to determine the order of theAR process

0 5 10 15 20 25

-1

-0.6

-0.2

0.2

0.6

1



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Block 3: Partial Autocorrelations (PACF) and the resulting correlograms from the LME Cash aluminium pricesafter being first differenced data obtained by using Stat graphics module of forecasting

PACF

LagsPartial Aut o-correlat ions

1 0

2 -0.0999

3 -0.1378

4 0

5 -0.0028

6 -0.0925

7 -0.0677

8 -0.0046

9 0

10 -0.2070

11 -0.0847

12 -0.0147

13 -0.1037

14 -0.0516

15 -0.0085

16 -0.0434

17 -0.0416

18 -0.1052

19 -0.0438

20 -0.0035

21 -0.0976

22 -0.1124

23 -0.0029

24 -0.0936

.2436

.0242

.1644

Partial Autoco rrelations PACF for 24 lags

In conclusion the analysis of the ACF and the PACF shows that the LME Cash aluminium prices fit an

ARMA (1, 1, 1) model, which could be defined as follows:

=*tY +11 tY +' 11 tt ee

AR(1) Constant MA(1)


0 5 10 15 20 25

-1

-0.6

-0.2

0.2

0.6

1

Observing at the plot of the first differenced time series partial autocorrelations wecan see that there are only one (1) PACF significantly different from zero at lag 1which could indicate an AR(1) process but also is observed that PACF do show adrop to a random value after p time lags instead of declining to zero exponentiallyafter many times lags, meeting the behavior exhibit in figure 4cfor ARMA processes,so in summary we have a mixture ARMA process, index there are severalautocorrelations after p time in the PACF plot, but to be a pure AR process PACFshould die out in a damped sine wave manner. Note that the PACF shows exactly 1nonzero autocorrelations in the tenth lag for a first order MA process.


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4.1.3 Estimation of the ARIMA model parameters (Third step)

Let denote the first differences of LME Cash aluminium prices. Then our tentatively identified ARMA

model is:

*

tY

=tY +11 tY +' 11 tt ee

Using Stat graphics forecasting module, we obtained the following estimates:* *

18.64846 0.0991822 0.163346t t tY Y e= + + 10te (2.1.10.4a)

4.1.4 Diagnostic checking (Fourth step)

After having estimated the parameters of a tentatively identified ARIMA model, it is necessary to do

diagnostic checking to verify that the model is adequate. There is basically two ways of doing this

(Makridakis , 1998, page 446):

1. Study the residuals, to see if any pattern remains unaccounted for.

2. Study the sampling statistics of the current optimum solution, to see if the model could be

simplified

In our case we will use the residuals checking, the residuals (errors) left over after fitting an ARIMA

model are, hopefully just random noise. Therefore if the autocorrelations and partials of the residuals

are obtained, we would hope to find no significant autocorrelations and no significant partials in the

process.

Using Stat graphicswe will performance three kind of tests to check randomness in the residuals,

three simple tests of the chosen model that we help us to see if the residuals estimated from this modelare white noise; if they are, we can accept the particular fit; if not, we must start over, the results of

these test are shown intable 9, as follows:



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Table 9: Diagnostic checking tests for the model at 90% of conf idence level

Test 1: Runs around the median:Median: 2.91621Number of runs around the median: 48Number of runs expected:50p-value: 0.7606

Test 2: Runs above and belowNumbers of runs above and below: 69Numbers of runs expected: 65.6667P-value = 0.495465Test 3:Test Box PierceTest based in the firs t 24 autocorrelationsP-value = 0.9809

Analysis:

A temporal series of random numbers is very often called a white noise, given that contains

contributions equals to many frequencies. The first test counts the number of times that the

sequence was above or below the median, the number of such executions or runs was equal to

48, compared to an expected value of 50 if the sequence had a random behavior, but given that

in this test the p-value is equal or greater to 0.10, the null hypothesis that the residuals are white

noise cannot be rejected. The second test counts the number of executions or runs that

sequence went up or down, the number of such executions was equal to 69, compared to the

expected value of 65.6667 if the sequence had a random behavior, but since the p-value for this

test is greater or equal to 0.10, the null hypothesis that the residuals are white noise cannot be

rejected at the 90% of confidence level or even greater. The third test is based in the sum of the

square of the 24 first autocorrelations coefficients, and since the p-value for this test is greater or

equal to 0.10, the null hypothesis that the series is random at 90% of confidence level cannot be

rejected.

4.1.5 Forecasting (Fifth step)We have to keep in mind that the Aluminium LME Cash prices data are for the period 1985I to

2009IV. Suppose, on the basis of model (2.1.10.4a), we want to forecast aluminium prices for

the first four quarters of 2010. By using Statgraphics we can make these calculationsroutinely, but we will explain step by step the process of loading the data into the software:


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38 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG

1. After we have load the time series data in the Statgraphics database file we will have the

data as follows intable 10:

QUARTERS Quartely

average LMECash ($/T)

QUARTERS Quartely

average LMECash ($/T)

QUARTERS Quartely

averageLME Cash

($/T)

QUARTERS Quartely

averageLME Cash

($/T)

1985Q1 1,089.63 1991Q2 1,321.02 1997Q3 1,638.18 2003Q4 1,512.86

1985Q2 1,081.23 1992Q3 1,255.01 1997Q4 1,579.54 2004Q1 1,649.73

1985Q3 1,005.33 1991Q4 1,127.46 1998Q1 1,463.36 2004Q2 1,677.26

1985Q4 986.65 1992Q1 1,241.46 1998Q2 1,363.77 2004Q3 1,708.75

1986Q1 1,134.03 1992Q2 1,299.80 1998Q3 1,321.16 2004Q4 1,828.06

1986Q2 1,170.58 1992Q3 1,295.90 1998Q4 1,283.03 2005Q1 1,899.88

1986Q3 1,152.70 1992Q4 1,179.98 1999Q1 1,195.64 2005Q2 1,789.76

1986Q4 1,142.64 1993Q1 1,186.65 1999Q2 1,305.65 2005Q3 1,828.84

1987Q1 1,278.33 1993Q2 1,132.60 1999Q3 1,442.52 2005Q4 2,075.59

1987Q2 1,430.67 1993Q3 1,163.22 1999Q4 1,500.55 2006Q1 2,420.33

1987Q3 1,737.00 1993Q4 1,073.74 2000Q1 1,642.93 2006Q2 2,653.00

1987Q4 1,831.00 1994Q1 1,244.51 2000Q2 1,477.18 2006Q3 2,481.16

1988Q1 2,172.07 1994Q2 1,333.96 2000Q3 1,564.50 2006Q4 2,720.12

1988Q2 3,055.38 1994Q3 1,505.67 2000Q4 1,513.59 2007Q1 2,602.73

1988Q3 2,628.86 1994Q4 1,822.98 2001Q1 1,576.90 2007Q2 2,761.78

1988Q4 2,428.53 1995Q1 1,927.26 2001Q2 1,501.01 2007Q3 2,546.00

1989Q1 2,218.10 1995Q2 1,797.25 2001Q3 1,379.71 2007Q4 2,443.21

1989Q2 2,099.74 1995Q3 1,836.39 2001Q4 1,318.58 2008Q1 2,742.13

1989Q3 1,757.39 1995Q4 1,661.71 2002Q1 1,381.36 2008Q2 2,939.57

1989Q4 1,729.79 1996Q1 1,597.79 2002Q2 1,356.05 2008Q3 2,786.71

1990Q1 1,516.64 1996Q2 1,552.99 2003Q3 1,310.63 2008Q4 1,820.98

1990Q2 1,539.42 1996Q3 1,443.15 2002Q4 1,352.94 2009Q1 1,359.46

1990Q3 1,806.50 1996Q4 1,428.72 2003Q1 1,396.89 2009Q2 1,484.94

1990Q4 1,545.55 1997Q1 1,596.14 2003Q2 1,380.46 2009Q3 1,811.85

1991Q1 1,505.26 1997Q2 1,585.11 2003Q3 1,436.35 2009Q4 2002.65

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2.Selection of the forecasting module, which is shown below in figure 5:

Figure 5:Forecasting module of Stat graphics


In the dialog box Data one must enter the selected column with the time series in question which is

LME Cash, then in the box Once every allows you to enter a unit of time (calendar or clock) and to

indicate the type of sampling interval which in our case is going to be Quarters, starting in Q1/85, below

in Number of Forecast we enter 4 for the four quarterly periods that we want to forecast ahead.


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3. Then the software will display the following screen(Figure 6) :Box of model specifications

options

Model:the model to which the other settings on the dialog box apply. Up to five forecasting models may

be considered at the same time, labeled A, B, C, D, and E.

Math:Before fitting a model, the data may be transformed using any of the indicated operations. With the

exception of the Box-Cox transformation, the selections are self-explanatory. The Box-Cox transformation

is used when necessary to make the data more Gaussian. For a detailed discussion, see the

documentation for the Box-Cox Transformations procedure.

Seasonal: seasonally adjust the data using the indicated method before fitting the model. Seasonal

adjustments are designed to remove any seasonal component from the data. The methods used are

discussed in the documentation for the Seasonal Decomposition procedure. In this case we enter 1 due to

the time series were differentiated once, according to the model ARIMA(1, 1, 1)

Inflation:adjusts the data for inflation using the specified inflation rate l before fitting the model.

Type:the type of forecasting model to be fit.


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Parameters and Terms:options for different forecasting models.

In our case for the ARIMA model we select AR(1) and MA(1)

Order:the number of terms in the Moving Average model.

AR, MA, SAR, and SMA:the order of the various components of the ARIMA models, referred to as p, q,

P, and Q respectively in the discussion below.

Optimize: whether optimal values of the parameters should be found. If checked, the parameter values

specified are used as starting values for the search procedures. If not checked, the values entered will be

used in the model.

Constant:whether a constant term should be included when fitting a Random Walk or ARIMA model.

Differencing: the order of seasonal and non-seasonal differencing to be applied when fitting the ARIMA

models, referred to as d and D in the discussion below.

Estimation Button: displays a dialog box that controls the nonlinear estimation procedure used when

optimizing the exponential smoothing and ARIMA models.

Regression Button: adds additional independent variables to the forecasting model when estimating a

trend or ARIMA model. Typically, such variables are lagged values of leading indicators.

Note:Whichever letter is selected in the Model field when the dialog box is closed is taken to be the

primary model. This is the model used when generating all of the tables and plots (except for the Model

Comparisons pane, which compares them all).



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4.2 Results of the time series modeling using Statgraphics(output):

Forecasting Aluminium LME Cash prices

Data variable: LME Cash

Number of observations = 100Start index = Q1/85Sampling interval = 1,0

Length of seasonality = 4

Forecast Summary

Nonseasonal differencing of order: 1

Forecast model selected: ARIMA(1,1,1) with constant

Number of forecasts generated: 4

Number of periods withheld for validation: 0

Estimation Validation

Statistic Period Period

RMSE 200,546

MAE 133,318

MAPE 7,55084

ME 0,0153564

MPE -0,338674

ARIMA Model Summary

Parameter Estimate Stnd. Error t P-value

AR(1) 0,0991822 0,404673 0,245092 0,806908

MA(1) -0,163347 0,401936 -0,4064 0,685353

Mean 9,60067 26,188 0,366606 0,714720

Constant 8,64846

Backforecasting: yes

Estimated white noise variance = 40218,9 with 96 degrees of freedomEstimated white noise standard deviation = 200,546

Number of iterations: 3

Conclusions

This procedure will forecast future values of LME Cash. The data cover 100 time periods. Currently, an autoregressive integratedmoving average (ARIMA) model has been selected. This model assumes that the best forecast for future data is given by a

parametric model relating the most recent data value to previous data values and previous noise. Each value of LME Cash hasbeen adjusted in the following way before the model was fit:



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Table of forecasts

Lower 95,0% Upper 95,0%Period Forecast Limit Limit

Q1/10 2047,39 1649,31 2445,47

Q2/10 2060,47 1419,33 2701,62

Q3/10 2070,42 1249,33 2891,51

Q4/10 2080,05 1111,36 3048,75

CommentsThis table shows the forecasted values for LME Cash. It displays the predicted values from the fitted model and the residuals(data-forecast). For time periods beyond the end of the series, it shows 95,0% prediction limits for the forecasts. These limits

show where the true data value at a selected future time is likely to be with 95,0% confidence, assuming the fitted model isappropriate for the data. You can plot the forecasts by selecting Forecast Plot from the list of graphical options. You can changethe confide

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MLPS_08 09 Sixto Lopez Report