mlps_08 09 sixto lopez report
Post on 03-Jun-2018
216 Views
Preview:
TRANSCRIPT
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
1/50
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
2/50
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.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
3/50
Sixto A Lopez D Industr ial Internship Final Report
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.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
4/50
Sixto A Lopez D Industr ial Internship Final Report
4 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
5/50
Sixto A Lopez D Industr ial Internship Final Report
5 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
6/50
Sixto A Lopez D Industr ial Internship Final Report
6 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
7/50
Sixto A Lopez D Industr ial Internship Final Report
7 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
8/50
Sixto A Lopez D Industr ial Internship Final Report
8 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
9/50
Sixto A Lopez D Industr ial Internship Final Report
9 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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:
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
10/50
Sixto A Lopez D Industr ial Internship Final Report
10 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
11/50
Sixto A Lopez D Industr ial Internship Final Report
11 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
2.0 Industr ial Project Development
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
12/50
Sixto A Lopez D Industr ial Internship Final Report
12 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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 $/ t (2004 - 2010)
Ao First Estimation Second Estimation Real LME Cash Variation (abs)
2004 1579 1715 1716 137
2005 1580 1816 1899 319
2006 1776 2100 2569 793
2007 2100 2650 2588 488
2008 2500 2700 2572 72
2009 2750 1415 1668 10822010 1500 1650 2200* 700
Average variation 513
*2010 forecast
Source: CVG Venal um Budget Department Services 2009
Over the years is observed that the Aluminium price has been recalculated due to the significant
differences between the approved price used and the real tendency of the price along the year.
This recalculation implies that more money have to be expended in overtime working hours to
reformulate the budget but also in meetings to obtain the new approval for the Board of Directors, but
above all, modifications imply expensive delays in projects and investments that could have been
carried out on time or not carried out at all.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
The quantification of the costs that imply annual Budget modifications will be seen with some detail
later on this paper, bearing the above in mind, the prime aim of this report is to analyze one time series
forecasting method in terms of their ability to forecast aluminium prices. The methodological
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
13/50
Sixto A Lopez D Industr ial Internship Final Report
13 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
approaches are tested using London Metal Exchange (LME) cash for aluminium over the period
firs t quarter 1985 four th quarter 2009.
One important factor that must be determined is what will it be the acceptable error in a forecast to
avoid a budget modification? Well, based on historical data we could established the error limit as
follows in table 2
HISTORICAL MAD VALUES OVER 300$/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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
14/50
Sixto A Lopez D Industr ial Internship Final Report
14 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
15/50
Sixto A Lopez D Industr ial Internship Final Report
15 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
16/50
Sixto A Lopez D Industr ial Internship Final Report
16 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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)
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
17/50
Sixto A Lopez D Industr ial Internship Final Report
17 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
18/50
Sixto A Lopez D Industr ial Internship Final Report
18 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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:
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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)
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
19/50
Sixto A Lopez D Industr ial Internship Final Report
19 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
20/50
Sixto A Lopez D Industr ial Internship Final Report
20 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
Source: Tudor (1997: 54)
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
21/50
Sixto A Lopez D Industr ial Internship Final Report
21 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
22/50
Sixto A Lopez D Industr ial Internship Final Report
22 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
23/50
Sixto A Lopez D Industr ial Internship Final Report
23 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
24/50
Sixto A Lopez D Industr ial Internship Final Report
24 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
25/50
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
26/50
Sixto A Lopez D Industr ial Internship Final Report
26 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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:
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
27/50
Sixto A Lopez D Industr ial Internship Final Report
27 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
28/50
Sixto A Lopez D Industr ial Internship Final Report
28 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
29/50
Sixto A Lopez D Industr ial Internship Final Report
29 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
30/50
Sixto A Lopez D Industr ial Internship Final Report
30 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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:
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
31/50
Sixto A Lopez D Industr ial Internship Final Report
31 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
32/50
Sixto A Lopez D Industr ial Internship Final Report
32 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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.
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
33/50
Sixto A Lopez D Industr ial Internship Final Report
33 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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)
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
34/50
Sixto A Lopez D Industr ial Internship Final Report
34 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
35/50
Sixto A Lopez D Industr ial Internship Final Report
35 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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)
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
36/50
Sixto A Lopez D Industr ial Internship Final Report
36 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG Venalum.
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:
CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
37/50
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:
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
38/50
Sixto A Lopez D Industr ial Internship Final Report
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
Venalum. CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
39/50
Sixto A Lopez D Industr ial Internship Final Report
39 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG
2.Selection of the forecasting module, which is shown below in figure 5:
Figure 5:Forecasting module of Stat graphics
Venalum. CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
40/50
Sixto A Lopez D Industr ial Internship Final Report
40 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVGVenalum. CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
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.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
41/50
Sixto A Lopez D Industr ial Internship Final Report
41 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG
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).
Venalum. CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
42/50
Sixto A Lopez D Industr ial Internship Final Report
42 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG
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:
Venalum. CONFIDENTIAL Privileged Information CVG Venalum proprietary information.
-
8/12/2019 MLPS_08 09 Sixto Lopez Report
43/50
Sixto A Lopez D Industr ial Internship Final Report
43 | 2010 - CVG Venalum All rights reserved for all countries. Cannot be disclosed, used, or reproduced without prior written specific authorization of CVG
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
top related