working paper cover proposal v5.1 - quantum global...

April 2018

1

Copper Price Forecasting Models Dr Jeremy Wakeford, Senior Macroeconomist, QGRL

April 2018

Contents Introduction .................................................................................................................................................. 2

Global Copper Market Dynamics .................................................................................................................. 3

Supply ........................................................................................................................................................ 3

Demand ..................................................................................................................................................... 8

Historical movements in copper prices .................................................................................................... 9

Futures prices .......................................................................................................................................... 11

Specification of Forecasting Models ........................................................................................................... 12

Univariate models ................................................................................................................................... 12

Models incorporating futures prices ...................................................................................................... 13

Structural models .................................................................................................................................... 14

Structural breaks and shocks .................................................................................................................. 16

Variables and Data ...................................................................................................................................... 16

Preliminary Data Analysis ........................................................................................................................... 17

Stationarity tests ..................................................................................................................................... 17

Graphical and correlation analysis .......................................................................................................... 19

Summary ................................................................................................................................................. 29

Model Results ............................................................................................................................................. 30

Univariate ARIMA models ....................................................................................................................... 30

Models based on futures prices .............................................................................................................. 33

Structural models .................................................................................................................................... 37

Comparison of ex post model forecasts ................................................................................................. 41

Ex ante forecast for 2018 ........................................................................................................................ 42

Conclusions ................................................................................................................................................. 43

References .................................................................................................................................................. 44

2

Introduction Copper has played a significant role in human society since the dawn of civilisation about 10,000 years

ago. First used for ornaments and coins, copper was subsequently fashioned into tools. Later, the

discovery that bronze could be formed as an alloy of copper and tin ushered in the Bronze Age circa 3,000

B.C. (Doebrich, 2009). Copper has several useful properties: it is malleable and ductile, it conducts

electricity and heat efficiently, and it is resistant to corrosion and has antimicrobial properties (ICSG,

2017). Consequently, the metal has a wide variety of applications in construction (such as wiring and

plumbing), electronic products, electricity generation and transmission, telecommunication networks,

industrial machinery, motors, transportation vehicles and semiconductors (Doebrich, 2009). Copper also

combines well with other metals to form useful alloys such as brass (with zinc), bronze (with tin) and

copper-nickel alloy (e.g. used in the construction of ships’ hulls to reduce corrosion).

These qualities help to explain why copper is today one of the world’s most important and widely traded

base metal commodities. International copper prices are determined on three commodity exchanges,

namely the London Metal Exchange (LME), the Commodity Exchange Division of the New York Mercantile

Exchange (COMEX/NYMEX) and the Shanghai Futures Exchange (SHFE). These exchanges enable

producers to sell to consumers through offers and bids, as per market participants’ understanding of

prevailing supply and demand conditions on a given day. The exchanges thus facilitate a transparent

process of price setting, for both spot prices and futures prices (ICSG, 2017).

Copper prices have fluctuated markedly over time, especially since the early 2000s (see Figure 1). There

are three main driving forces underlying price trends: (1) supply side factors (such as mine production,

recycling rates, refinery capacity and utilisation, and refined copper stocks); (2) demand side factors (e.g.

rates of economic growth and industrial production in the world at large and especially in key consuming

countries such as China); and (3) speculative trading by commodity traders and asset managers. Being

able to predict the future path of copper prices would assist in economic planning and investment

decisions involving infrastructure and products that use copper intensively, as well as copper commodity

trading. Hence, there is a need for reliable copper price forecasting models.

This paper seeks to develop econometric models that forecast copper prices on a monthly basis, up to

twelve months into the future. Three main types of models are developed: univariate time series models,

which use only the information contained in historical copper price series; models incorporating futures

prices to help predict future spot prices; and structural time series models, which relate copper prices to

various determinants, including fundamental drivers and financial variables.

The paper is organised as follows. The first section provides details on the global copper market, including

supply, demand and historical price movements. The second section outlines the three types of

econometric models, while subsequent sections describe the variable and data, and conduct preliminary

analysis of the relevant time series. The fifth section presents the modelling results and compares their

ex post forecast performance, and presents ex ante forecasts for 2018. The final section concludes.

3

Global Copper Market Dynamics

Supply

Copper occurs mainly in two types of deposits (Doebrich, 2009). The most important is Porphyry copper

deposits, associated with igneous intrusions, which are the source of approximately two-thirds of the

world’s copper supply. Significant Porphyry copper deposits are located in mountainous areas of western

North and South America. The other main type of copper deposit is that found in sedimentary rocks, such

as in the central African copper belt. Sedimentary copper deposits contain about a quarter of global

copper resources. Figure 1 shows the global distribution of known Porphyry and sedimentary copper

deposits as of 2008.

Figure 1: Global distribution of known copper deposits in 2008

Source: Doebrich (2009)

An assessment of global copper deposits by the United States Geological Survey (USGS) in 2014 estimated

that identified resources (i.e., geologically identified resources that could be extracted with current

technologies) contained approximately 2.1 billion tons of copper (USGS, 2018). Reserves, which depend

on prevailing economic conditions, including prices, as well as technologies available to extract copper,

were estimated at 794 million tonnes (mt) in 2017, representing 40 years of supply at current rates of

production. Chile is the top reserve holder, with an estimated 170 mt, followed by Australia (88 mt) and

Peru (81 mt) (see Table 1). The Democratic Republic of Congo (DRC) and Zambia each have estimated

reserves of 20 mt, which would sustain these countries’ 2016 levels of production for 24 years and 26

years, respectively.

4

Historically, the estimated quantities of copper reserves and resources have trended upwards as a result

of continued geological exploration, improved mining technologies and changing economics. Since the

1950s, reserves have continually been at a level that would meet 40 years of the then prevailing demand

(ICSG, 2018). Improvements in copper recycling have also contributed to annual supplies. The USGS (2018)

estimates that are about 3,500 mt of undiscovered copper resources. As a result of all these factors, there

is not likely to be any major resource constraint on copper supplies in the foreseeable future.

Nevertheless, the continued depletion of high-grade ores will tend to raise production costs – although

improvements in mining technologies could temper this.

Table 1: World’s leading mined copper producers (2016) and reserve holders (2017)

Country Production

(kt)

Reserves

(mt)

Chile 5 550 170

Peru 2 350 81

China 1 900 27

United States 1 430 45

Australia 948 88

D.R. Congo 846 20

Zambia 763 20

Mexico 752 46

Indonesia 727 26

Canada 708 11

Other Countries 4 160 260

World 20 134 794

Source: USGS (2018)

The United States was the world’s foremost copper producer until 2000, when Chile took over the top

spot on the rankings. The USGS estimates that Chile accounted for 27% of copper output in 2017, followed

by Peru (12%), China (9%) and the US (7%) (Figure 2). Africa’s top copper producers, DRC and Zambia,

each contribute about 4% of global copper supply. The top 10 producers account for over three-quarters

of global supply.

Global copper mine output has grown at an average annual rate of 3.2% since 1900 (Figure 3). The bulk

of copper has historically been produced through metallurgical treatment of concentrates. From the

1960s onwards, copper has also been extracted through leaching (solvent extraction) and electrowinning

(SX‐EW process), from primarily low grade oxide ores and also some sulphide ores (ICSG, 2017). However,

primary production of copper contracted by over 2% in 2017, the first substantial decline in more than 15

years. This follows several years of low investment in production capacity as a result of low copper prices.

The only major new mining project set to come on stream in the coming few years is First Quantum’s

Cobre Panama mine.

5

Figure 2 : Shares of world copper mine production by country, 2017 (estimated)

Source: USGS (2018)

Figure 3 : World copper mine production, 1900-2016 (thousand tonnes)

Source: ICSG (2017)

Chile27%

Peru12%

China9%

United States7%

Australia5%

D.R. Congo4%

Zambia4%

Mexico4%

Indonesia3%

Canada3%

Other Countries22%

6

In addition to primary copper production from mining, so-called secondary copper is produced from

recycled metal. Copper can be readily recycled because the metal and its alloys can be melted down

without loss of their physical or chemical properties (ICSG, 2017). Since almost all products manufactured

from copper can be recycled, it is among the most recycled of all metals. Since 2011, secondary copper

has comprised around 17-18% of total refined copper production (see Table 2).

Table 2 : World copper production and usage trends

2011 2012 2013 2014 2015 2016

World mine production 15 964 16 691 18 185 18 432 19 148 20 357

Mine capacity utilisation (%) 82.1 83.4 87.6 85.5 85.2 86.7

Primary refined production 16 133 16 598 17 255 18 576 18 925 19 473

Secondary refined production 3 468 3 596 3 803 3 915 3 945 3 866

Total refined production 19 601 20 194 21 058 22 491 22 870 23 339

Secondary Refined as % in Total Prod. 17.7 17.8 18.1 17.4 17.3 16.6

World refined usage 19 713 20 473 21 396 22 885 23 040 23 507

World refined stocks 1 205 1 376 1 325 1 350 1 521 1 391

Period stock change 7 171 -52 25 171 -130

Refined balance -113 -279 -337 -394 -169 -168

LME Copper Price 8 811 7 950 7 322 6 862 5 494 4 863

Source: ICSG (2017)

As can be seen in Figure 4, global output of refined copper has been steadily increasing over the past

several decades, with a particularly rapid growth rate over the last 10 years.

Figure 4: World refined copper production, 1900-2016 (thousand tonnes)

Source: ICSG (2017)

7

Supply outlook, risks and challenges

Copper mine capacity is anticipated to grow by an average rate of 2.5% per annum in the coming few

years, as new capacity is added at certain existing mines and some new operations come on stream (ICSG,

2017). Provided the capacity utilisation rate remains steady, as it has done in recent years (see Table 2),

then global copper mine supply should grow at a similar rate of about 2.5% per annum.

In general, the fact that copper production is geographically dispersed across the globe means that the

risk of major supply disruptions is relatively low, at least compared to minerals that occur in more

concentrated deposits (Doebrich, 2009). Nevertheless, disturbances to supply chains can and do occur

from time to time. There are approximately 700 copper mines in operation globally, the largest 20 of

which contribute about half of world production (Dizard, 2018). Thus, a disruption at one or more of the

biggest mines can have an impact on prices. For example, in 2017 various supply issues – mainly declining

ore grades and labour disputes – resulted in a 2.5% decline in global mine production, which in turn

contributed to the rise in copper prices (USGS, 2018). In particular, copper mining in Chile – the source of

over a quarter of world mine output – is subject to periodic labour disputes, which can affect the global

market. In early 2018, there were labour disputes at mines accounting for over 75% of Chile’s production

capacity (Dizard, 2018).

Another important dynamic in the copper market is that the supply response to rising copper prices is

rather slow. This is because the lead time from an investment decision to commission a new mine to

actual production can be many years, even decades in some cases (Dizard, 2018).

Copper mining has occurred for millennia, and consequently many of the most easily accessible deposits,

and those with the highest ore grades, have already been exploited. Increasingly, the frontier for new

copper mines is in more challenging environments, such as underground or in logistically remote areas

such as central Africa. These factors tend to raise the costs of production. For lower ore grades and sub-

surface mining, more capital has to be invested per tonne of copper produced, raising operating costs.

Furthermore, the cost of capital may rise in times of protracted price volatility, reflecting increased risk

perceptions surrounding new and existing mining ventures (ICSG, 2017).

Tighter tax and royalty regimes can also affect supply by influencing investment decisions. For example,

in late 2017 the DRC parliament passed a new mining code that raises taxes and royalties due by mining

companies – although as of this writing it has yet to be signed into law by President Joseph Kabila. In

January 2018 the CEO of the state mining company, Gecamines, stated his intention to renegotiate all

contracts with foreign mining firms in the next year, in order to garner a larger share of revenues for the

DRC (Aglionby & Hume, 2018). This applies mainly to cobalt and copper mines in the country’s south.

However, recent research suggests that, in general, tax regimes are less significant than resource

endowments and quality (ICSG, 2017). Other constraints on new mines include stricter environmental

regulations in many countries, which can delay the start-up of new projects, as well as skilled workers

capacity constraints.

8

Demand

Copper consumption has grown steadily over the past century, rising from under 500,000 tonnes in 1900

to 23.5 mt in 2016 – representing a compound annual growth rate of 3.4% per annum (Figure 5). Between

1980 and 2008, consumption of copper declined slightly in the advanced economies, but grew strongly in

many emerging economies, especially China and India. China surpassed the United States as the top

consumer of refined copper in 2002 (USGS, 2018), and since then has come to dominate the global market.

World usage of refined copper reached 23.5 million tonnes in 2016, up from 19.7 mt in 2011 (Table 2).

Figure 5: Copper production and usage, 1960-2016

Source: ICSG (2017)

In 2016, Asia accounted for over two-thirds (69%) of world refined copper usage, whereas Europe’s share

was 18% and North America’s, 10%. China’s apparent consumption of refined copper was about 11.7 mt

in 2016, i.e. 50% of the world total (ICSG, 2018).

Figure 6: Refined copper usage by region, 2016

Source: ICSG (2017)

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Asia’s share of global copper smelter production climbed from 27% in 1990 to nearly 60% in 2016, mainly

as a result of rapidly growing smelter output in China (ICSG, 2017). Asia is the only region of the world

that has seen a significant and sustained increase in smelter capacity over the past two decades. Europe

had a slight increase in the late 1990s, while American capacity declined at the same time. These trends

reaffirm Asia’s – and especially China’s – centrality on the demand side of the copper market. China

accounted for more than one-third of global copper smelter output in 2016, followed by Japan and Chile

with 8% each (ICSG, 2017). Cuddington and Jerrett (2008) found evidence to support the hypothesis of a

Chinese-driven commodity price super-cycle in the early 2000s.

There are several major long-term drivers of demand for copper. The most basic are growth in the world

population and in developing economies, where there is a great need for basic infrastructure that relies

on copper, as well as copper-containing devices, machines and vehicles. A more specific driver is the

transition from fossil fuels to renewable energy sources, which increases the need for copper for

generation equipment and transmission cables. This shift is compounded by the transition from internal

combustion engine vehicles to electric vehicles, as the latter require more copper (Dizard, 2018).

If copper supplies were constrained relative to demand, forcing up prices, this could induce a substitution

of other materials for copper. Substitutes are available for several applications of copper (USGS, 2018):

“Aluminum substitutes for copper in power cable, electrical equipment, automobile radiators, and cooling

and refrigeration tube. Titanium and steel are used in heat exchangers. Optical fibre substitutes for copper

in telecommunications applications, and plastics substitute for copper in water pipe, drain pipe, and

plumbing fixtures.” Such substitution could restrain longer-term increases in the copper price, although

aside from pricing, copper is still the material of choice for these applications.

Historical movements in copper prices

Figure 7 clearly shows that the price of copper closely tracks the metals price index over the entire period

1960 to 2017. This is confirmed by the pairwise correlation coefficient of 0.97. This close association is

hardly surprising, given that copper is the largest component of the base metals price index, with a weight

of 38.4%. However, it does also show that copper prices follow similar broad trends and fluctuations to

the other base metals.

Historically, the trend in the nominal copper price can be split into two eras, before and after 2003. Up

until that year, there was a very gradual upward trend in nominal prices, but in fact a downward trend in

real copper prices. Beginning in 2003, there was a rapid acceleration in the nominal price, which rose from

US$1,687 per tonne in June of that year to US$8,414 per tonne in July 2008. The abrupt change coincided

with the entry of China into the global market as a net copper importer, and the Asian country’s double-

digit rates of economic growth during the ensuing years. This development was part of a general trend of

rapidly rising demand amidst stagnant supply across many commodity markets in the early 2000s (see

Hamilton, 2009; Kilian, 2009). The dramatic copper price rise was also fuelled by a speculative commodity

10

bubble, which swept up most commodities in 2007-2008 (Irwin, Sanders & Merrin, 2009).1 This was

followed by a sudden and spectacular price collapse (to US$3,072 per tonne) in late 2008, as a result of

the collapse in asset prices and world demand in the wake of the Global Financial Crisis (GFC).

Subsequently, the copper price rebounded swiftly and peaked at US$9,869 per tonne in February 2011.

This surge was driven partly by the cyclical recovery in economies and asset markets following

unprecedented and coordinated intervention by monetary authorities in the major economies. In

addition, the strong price recovery was fuelled by a rapid rise in Chinese demand, propelled by the

country’s massive fiscal stimulus package, which centred on infrastructure investment and construction –

both of which are copper intensive. For the next few years, the price of copper gradually receded as the

Chinese economy's rate of growth decelerated. This price decline continued until January 2016, after

which time the copper price has gradually risen again as Chinese and global demand has picked up steam.

As shown later in the report, fluctuations in the value of the US dollar against other currencies has also

played a significant role in movements in copper prices over the past 15 years.

Figure 7: Copper price and base metals price index

Source: World Bank

As described above, Chinese demand has had a major influence on global copper prices over the past 15

years. With China still consuming about half of the world’s supply, it will likely continue to be the main

price driver for the foreseeable future, aside from possible financial shocks. Structural forecasting models

therefore need to take Chinese demand into account. Other large emerging economies, such as India and

Indonesia, are also becoming increasingly important sources of copper demand.

1 Cheng and Xiong (2014) argue that risk sharing and information discovery provided two economic mechanisms through which financialisation affected commodities markets.

0

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1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 20152

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Futures prices

Futures prices for commodities are assumed to reflect the collective expectation of market participants

about where the price will settle at a future date, based on all currently (publicly) available information

and taking into account a risk adjustment. For example, the futures price for copper may be expected to

reflect the ‘collective wisdom’ of suppliers, consumers and traders about where the spot price will be

upon the expiry of the futures contract. Thus the 3-month futures price should, in theory, predict the level

of the spot price in 3 months’ time, although there may be a differential based on the expected return

that investors require (alternatively, a compensation for bearing the risk). Instead of purchasing copper

forward, investors could earn interest in low-risk assets such as US Treasury bills. Therefore, the interest

rate on T-bills can be seen as a proxy for the return commodity investors will expect. In a very low interest

rate environment, therefore, the spread between the expected spot price and the futures price will be

smaller than in periods when interest rates are higher.

Figure 8: Copper spot and futures prices, 2000-2017

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

2000 2002 2004 2006 2008 2010 2012 2014 2016

CPS CPF03

CPF15 CPF27

Source: Bloomberg

Figure 8 displays the spot price of copper (CSP) and the prices of three futures contracts at 3 months

(CPF03), 15 months (CPF15) and 27 months (CPF27) ahead. What is really striking about the chart is the

way that a spread opened up between the three futures contracts from early 2004 (when the big

acceleration in prices began) until August 2008 (when prices collapsed following the Global Financial

Crisis), after which point the spread almost disappeared. The situation in which futures prices are below

expected spot prices is known as “backwardation”. Thus the copper market was in a very large

backwardation between 2004 and 2008. This could potentially be explained by the fact that US interest

rates rose during this period, but were lowered dramatically during the GFC and have remained very close

12

to zero for much of the period since then. Generally, commodity traders buying forward contracts would

expect a return benchmarked on the interest rate on risk-free assets. Therefore, the expected return in

terms of the spread between the futures price and the expected spot price at the time of contract maturity

should be at least as large as the risk-free rate of interest.

Figure 9 plots the US federal funds rate (USFFR) along with the spread between the spot and 15-month

futures prices of copper. It does seem that, overall, there is some association between the two series,

although there is clearly a lot of volatility in the copper price spread that cannot be explained by the

interest rate.

Figure 9: Copper futures-spot price spread and US interest rate

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Specification of Forecasting Models

Univariate models

According to the Efficient Market Hypothesis (EMH), asset prices fully incorporate and reflect all

information available to market participants at a given point in time. This implies that market prices should

only react to new information, or ‘shocks’, and that traders should not be able to consistently ‘beat the

market’. This theory underpins the view that many asset prices should follow random walk processes,

such that the best prediction of tomorrow’s price is today’s price, assuming that there is no systematic

‘drift’. If there is drift (e.g. reflecting expectations of positive returns or underlying economic growth),

then the forecast for each period ahead will merely increase (or decrease if the drift term is negative) by

13

the amount of the drift parameter. We test the random walk hypothesis in the case of copper prices in

the next section using standard unit root tests, which are based on the following simple model:

CPSt = α + βCPSt-1 + δT + et (1)

where CPSt is the current spot price, T is a deterministic trend, α is a drift parameter and et is a white

noise error process. If β = 1, the copper price series contains a unit root and should be modelled as a

difference stationary process. If β < 1, the price series is stationary in levels and follows a first-order

autoregressive process, AR(1). More generally, we can allow for a higher-order AR process as well as a

moving average error term, as follows:

ΔdCPSt = α + ∑βpΔCPSt-p + ut + ∑λqUt-q (2)

where ut is white noise. The above model is an ARIMA(p,d,q), where d represents the order of integration

of the CPS series.

Models incorporating futures prices

As noted earlier, commodity futures prices are assumed to incorporate all available information about the

future direction of spot prices. If, for example, today’s 3-month futures prices are higher than current spot

prices, then this is taken to indicate that market participants expect an upward movement in spot prices

over the ensuing three months. Conversely, 3-month futures prices below current spot prices should

indicate that the market anticipates a decline in spot prices. Thus, in theory, futures prices are commonly

regarded as a reliable guide to the likely path of spot prices, and can therefore be used in forecasting

models. Under the efficient market hypothesis, futures prices are expected to be unbiased predictors of

future spot prices. Thus a simple forecast model can be expressed as follows (Bowman & Husain, 2004):

CPSt = α + βCPFt|t-k + et (3)

where CPFt|t-k is the price in period t that is implied by the futures market in period t-k. In other words,

the futures price in period t is used to predict the spot price in period t+k, where k is the length of the

futures contract in months. The appropriate modelling strategy is to test for the presence of unit roots in

both CPSt and CPFt, and if both series are nonstationary, to test for cointegration. If evidence of

cointegration is found, then a Vector Error Correction Model (VECM) can be estimated, which

incorporates the long-run relationship between the two price series as well as short-run dynamics. The

VECM can then be used for forecasting CPSt. The specification of the VECM is as follows:

ΔCPSt = αs + β0sεt-1 + ∑βiΔCPSt-i + ∑γjΔCPFt-j + ut (4a)

ΔCPFt = αf + β0fεt-1 + ∑δiΔCPSt-i + ∑θjΔCPFt-j + vt (4b)

where the error correction term is εt-1 = CPSt-1 – λCPFt-1

14

Structural models

Structural econometric models take into account variables that are regarded as determinants of, or are

expected to influence, the series of interest, in our case copper spot prices. They may also include

economic variables that serve as indicators of financial market activity and expectations of future market

movements. Thus, structural explanatory variables can be divided into ‘fundamental’ factors (supply,

demand and inventory variables) and financial variables (such as proxies for global risk appetite and

financial market activity) (Buncic & Moretto, 2015). The financialisation of commodities, including copper,

has been driven by legislation governing futures trading as well as trends within markets, such as the

substitution of copper for gold and silver in asset portfolios (Buncic & Moretto, 2015). The explanatory

variables considered in our forecasting models are briefly described below. For the purposes of

forecasting models, our preference is for monthly data series, and this imposes some constraints on the

variables that can be included, since some variables are available only with an annual or quarterly

frequency.

Fundamental variables:

Since China accounts for around half of world copper consumption, but less than 10% of copper mine

output, it is expected that China’s imports of copper products have a major impact on global copper

prices. Since 2004, China has been a net importer of both unrefined copper (copper ores and

concentrates) and refined copper.

China's demand for copper is related mainly to infrastructure investment, manufacturing and

construction activity. We use as a proxy for this demand the growth in China’s industrial production

index (CHIP). In addition, we investigate the usefulness of industrial production growth in India and

the Advanced Economies as alternative demand-side variables. Issler et al (2014: 310) demonstrate

“theoretically that there must be a positive correlation between metal-price variation and industrial-

production variation if metal supply is held fixed in the short run when demand is optimally chosen

taking into account optimal production for the industrial sector.” They confirm this empirically with

“overwhelming evidence that cycles in metal prices are synchronized with those in industrial

production”.

The supply of copper tends to be very inelastic, since as mentioned earlier it takes several years at

least for a new copper mine to be developed. Supply shocks can trigger price cycles that occur over a

number of years (Labys et al., 2000, in Buncic & Moretto, 2015). However, global copper supply data

is available only on an annual basis; hence it is not useful for short-term forecasting models based on

monthly time series.

Financial variables:

The strength of the US dollar relative to other major currencies has a major influence on dollar-

denominated commodity prices (Akram, 2009). Hence we investigate the influence of the US dollar

index (USD), expecting a positive relationship between the dollar index (measured in terms of dollars

per foreign currency unit) and copper prices. For example, if the dollar weakens relative to other

currencies as a result of domestic economic conditions in the US, then commodity prices should rise

in dollar terms so that the price in foreign currency units remains the same.

15

The exchange rate of major copper producing countries may be expected to provide information

about the future supply of copper from those countries and also expectations of future copper prices.

Evidence for the capacity of commodity currencies to predict commodity prices is provided by Chen

et al. (2010). We therefore follow Buncic and Moretto (2015) in investigating the significance of the

Chilean peso (CLPESO).

The oil price (OILP) is also tested for co-movement with the copper price. Although oil prices may

influence the cost of copper production (since oil is used to fuel mining equipment and

transportation), this effect is probably marginal. However, we expect a close association between the

two series due to general economic factors at work in commodity markets, which are expected to

drive oil and copper prices in similar directions.

The Baltic Dry Index (BDI) is a composite index reflecting average time-charter hire rates for three

sizes of ocean-going vessels, namely Capesize, Panamax and Supramax, along 20 main shipping

routes. The BDI therefore provides an indicator of global dry bulk shipping costs, and also serves as a

proxy for the global shipping market and hence international trade.

The S&P 500 share price index (SP500) is one of the standard benchmarks of international equity

markets, and serves as a gauge of investor sentiment. Hence, it is expected to be positively correlated

with the prices of internationally traded commodities, including copper.

The volatility index (VIX) provides an indicator of risk appetite on global asset markets. The challenge

with using the VIX as an explanatory variable in a standard linear regression model is that volatility is

high when assets prices are either increasing rapidly or decreasing rapidly. Therefore, it is unlikely to

be correlated well with a commodity price such as copper, which has undergone large upswings and

downswings during the period under review.

The general structural model including the above explanatory variables would looks as follows:

CPSt = α + β1IPt + β2USDt + β3CLPESOt + β4OILPt + β5SP500t + β6BDIt + et (5)

where IP = industrial production of a relevant country or group of countries, and the other variable names

are defined in Table 3 below. Each explanatory variable may be lagged by one or more months, depending

on whether its movements precede those of copper prices. In general, fundamental factors are expected

to have slower-moving impacts on copper prices (i.e., prices may take several months to reflect changes

in demand and supply conditions), while financial drivers can result in short-term volatility since

commodity traders react to news immediately. In the empirical section we employ Autoregressive

Distributed Lag (ARDL) models, which extend (5) by allowing for lagged values of both the dependent

variable and the explanatory variables on the right hand side. The ARDL framework allows us to test for

cointegration among a set of I(1) (nonstationary) and I(0) (stationary) variables.

In theory, structural models such as (5) can be used for ex ante static forecasting, provided the explanatory

variables are all lagged and/or can themselves can be reliably forecast into the future. However, in the

latter case this may be onerous in terms of the number of additional forecasting models that are required

for the individual structural variables.

16

Structural breaks and shocks

There are two important empirical issues to consider before embarking on the forecasting model-building

exercise, namely structural breaks and exogenous shocks. First, as shown in Figure 7, there is a clear

structural break in the copper (spot) price series in 2003/4, when China became a net importer of copper.

The fundamental dynamics in the copper market changed at this time, with prices rising dramatically and

becoming far more volatile. Therefore, we will focus on the subsequent period for building forecasting

models. Clearly, in order to generate reliable forecasts, models should be based on prevailing structural

market dynamics. Second, major swings occurred in the copper price between mid-2008 and mid-2009,

when the price plunged steeply and then rebounded rapidly. The collapse was triggered by the Global

Financial Crisis, which resulted in a massive sell-off of financial assets as well as a 25 per cent collapse in

global trade as the international trade payments system (letters of credit) partially froze. Subsequently,

copper demand rebounded following the Chinese government’s massive stimulus package, which boosted

infrastructure and construction spending. It may be necessary to include a dummy variable for the period

August 2008 to May 2009, to account for this extraordinary event. Alternatively, the sample period could

be reduced, to begin only in 2010. A third approach is to include structural variables that capture the 2008

downturn and subsequent recovery.

Variables and Data Table 3 provides a list of the time series variables used in the forecasting exercise, including both price

series and explanatory variables used in the structural models. The source for all data series is Bloomberg,

unless otherwise indicated. The series are of a monthly frequency, using end-of-period values (i.e. last

trading day of the month) when the underlying data were daily series. Copper spot and futures prices are

those quoted on the London Metals Exchange.

Table 3: List of time series variables with descriptions and units

Variable Name Description Units

CPS Copper spot price USD per tonne

CPF03 Copper 3-month futures price USD per tonne



AEIP Advanced economies industrial production1 Year-on-year growth rate

CHIP Chinese industrial production Year-on-year growth rate

INIP Indian industrial production Year-on-year growth rate

CHCOPIMP Chinese copper imports (ores & concentrates) Tonnes

CHRCOPIMP Chinese refined copper imports Tonnes

OILP Brent crude oil price USD per barrel

USD US dollar index USD per foreign currency unit

CLPESO US dollar/Chilean peso exchange rate USD per CLP

BDI Baltic Dry Index Index

SP500 S&P 500 stock index Index 1This series was drawn from the IMF’s International Financial Statistics database.

17

Preliminary Data Analysis

Stationarity tests

The first step in time series modelling is to determine the stationary properties of the data. This is

performed for copper spot and futures price series using the Augmented Dickey-Fuller (ADF) and Phillips-

Perron (PP) tests for unit roots, both of which have a null hypothesis of a unit root being present (i.e. the

series is nonstationary). These tests may be sensitive to the choice of sample period, with a longer sample

generally being preferred. However, the tests are also sensitive to structural breaks, in which case it may

be preferable to reduce the sample period to exclude clearly defined breaks. As stated above, our

preferred sample period is 2003M01 to 2017M12, which is a 15-year period containing 180 monthly

observations. Both ADF and PP tests consistently fail to reject the null hypothesis of a unit root

(nonstationarity) for all four spot and futures price series in their levels, but reject the null for the first

difference of each series. Hence, the evidence suggests that copper spot and futures price series each

contain one unit root, i.e. are integrated of order one.

Table 4 : Unit root tests for copper prices (2003:01-2017:12)

Price Series Augmented

Dickey-Fuller

t-statistic

[p-value]

lag length Phillips-Perron

t-statistic

[p-value]

bandwidth

Spot -2.24

[0.19]

0 -2.39

[0.15]

3

first difference -11.51*

[0.00]

0 -11.50*

[0.00]

1

Futures (3-month) -2.19

[0.21]

0 -2.35

[0.16]

4


[0.00]

0 -11.60*

[0.00]

2


[0.28]

0 -2.18

[0.22]

5


[0.00]

0 -11.77*

[0.00]

3


[0.33]

0 -2.04

[0.27]

5


[0.00]

0 -12.15*

[0.00]

4

Notes:

Null hypothesis: series contains a unit root.

18

For the ADF tests, lag lengths were determined by minimizing the Schwarz information criterion. An

intercept was included in the test specification, but not a deterministic trend (which was found to be

highly statistically insignificant in all cases).

For the PP tests, Bartlett kernel estimation is used and bandwidth estimations are made according to

the Newey-West (1994) procedure.

* Significant at the 1% level.

Table 5 : Unit root tests for structural variables

Series Sample Period Augmented

Dickey-Fuller

t-statistic

[p-value]

Lag

length,1

Constant,

Trend

Phillips-Perron

t-statistic

[p-value]

Band-

width,2

Constant,

Trend

CHIP 2003:01-2017:12

2006.07-2017.12

-4.12 [0.01]

-0.98 [0.76]

-3.89 [0.02]

-1.84 [0.36]

5, C, T3

3, C

5, C, T3

4, C

-3.92 [0.01]

-1.42 [0.57]

-3.12 [0.11]

-1.95 [0.31]

1, C, T3

6, C

1, C, T3

2, C

INIP 2003:01-2017:12

2006.07-2017.12

-2.04 [0.27]

-1.78 [0.39]

12, C4

12, C4

-2.50 [0.12]

-2.21 [0.20]

5, C4

4, C4

AEIP 2003:01-2017:12

2006.07-2017.12

-3.75 [0.01]

-4.74 [0.00]

6, C4

2, C4 -3.02 [0.03]

-2.65 [0.09]

9, C4

8, C4

USD 2003:01-2017:12

2006.07-2017.12

-1.52 [0.52]

-2.47 [0.35]

0, C

0, C, T

-1.68 [0.44]

-2.65 [0.26]

5, C

5, C, T

CLPESO 2003:01-2017:12

2006.07-2017.12

-2.17 [0.22]

-1.66 [0.45]

0, C4

0, C4

-2.17 [0.22]

-1.70 [0.43]

0, C4

1, C4

OILP 2003:01-2017:12

2006.07-2017.12

-2.38 [0.15]

-2.36 [0.15]

1, C4

1, C4 -2.18 [0.21]

-2.00 [0.29]

4, C4

4, C4

SP500G 2003:01-2017:12

2006.07-2017.12

-3.06 [0.03]

-2.32 [0.17]

1, C4

1, C4

-3.26 [0.02]

-2.56 [0.10]

7, C4

6, C4

BDI 2003:01-2017:12

2006.07-2017.12

-2.76 [0.07]

-2.40 [0.14]

1, C5

1, C5

-2.28 [0.18]

-1.95 [0.31]

7, C

8, C

Notes:

Bold t-statistics and p-values indicate rejection of the null hypothesis of nonstationarity at the 5% level. 1 Lag lengths were determined by minimizing the Schwarz information criterion. 2 Bartlett kernel estimation is used and bandwidth estimations are made according to the Newey-West

(1994) procedure. 3 Coefficient on deterministic trend was significant in test regression, and therefore trend was included. 4 Trend was not significant in test regression, and in most cases did not affect the result of the unit root

test. 5 Although the trend term was significant in the test regression, the graph shows no evidence of a

deterministic trend.

19

According to the balance of evidence in the unit root tests above, we can conclude the following about

the order of integration of the series:

CHIP is I(0) when a deterministic trend is included, and I(1) without a trend

INIP is I(1), which is somewhat surprising considering that the series is a growth rate

AEIP is I(0)

USD is I(1)

CLPESO is I(1)

OILP is I(1)

SP500G is I(0) for the period 2003-2017

BDI is I(1)

In almost all cases, the test result does not change when we restrict the sample period to begin in

2006M01 instead of 2003M01. The one exception is SP500G. Since unit root tests have lower power

when the time span is short (i.e., there is a greater chance of not rejecting a false null hypothesis), as

well as the fact that SP500G is a log-differenced series, it seems reasonable to assume the series is I(0).

Graphical and correlation analysis

Chinese refined copper imports

Contrary to expectations, the charts below show that, by and large, there is no clear relationship between

Chinese copper imports and copper prices – aside from the strong rebound in prices in 2009, which were

preceded by a massive spike in refined copper imports. Unrefined copper imports began in 2004 and have

shown a gradual upward trend ever since. Refined copper imports have been more volatile, but have also

trended upwards – driven by China’s economic growth. (Both import series have been smoothed with 3-

month moving averages to highlight the trends and cycles.) These charts suggest that financial conditions

may be more important drivers of copper price movements than fundamentals like Chinese demand for

the metal. Indeed, copper spot prices are negatively correlated with both unrefined (r = -0.27) and refined

(r = -0.26) Chinese copper imports. Consequently, these variables are not expected to provide any

predictive power for forecasting copper prices. Instead, we analyse industrial production as a more

general proxy for demand.

Table 6 : Correlation matrix for copper price and Chinese copper import growth

CPS CHCOPIMPGS CHRCOPIMPGS CPS 1.000000 -0.274703 -0.258048

CHCOPIMPGS -0.274703 1.000000 0.270902 CHRCOPIMPG

S -0.258048 0.270902 1.000000

20

Figure 10: Copper price and Chinese copper imports

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

800,000

900,000

03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS CHCOPIMPS CHRCOPIMPS

Figure 11: Copper price and growth in Chinese copper imports

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

-200

-100

0

100

200

300

400

500

600

05 06 07 08 09 10 11 12 13 14 15 16 17

CPS CHRCOPIMPG

CHRCOPIMPGS CHCOPIMPGS

21

Industrial Production

Figure 12 displays industrial production (IP) indices for the Advanced Economies, China and India. All three

series represent growth rates of industrial production, and have been smoothed using three-month

moving averages in order to reduce excessive volatility and to highlight trend and cyclical features. Over

the period 2003M01 to 2017M12, China’s IP index is reasonably well correlated with India’s (0.63), but

weakly correlated with industrial production in the Advanced Economies (0.29). All three indices exhibit

a major slump in 2008-2009, coinciding with the Global Financial Crisis. However, China weathered the

crisis considerably better than the Advanced Economies and India.

Figure 12: Industrial production in Advanced Economies, China and India

Table 7 : Correlation matrix for industrial production indices

CHIP INIP AEIP CHIP 1.000000 0.629977 0.293658

INIP 0.629977 1.000000 0.536816

AEIP 0.293658 0.536816 1.000000

-25

-20

-15

-10

-5

0

5

10

15

20

25

20

01

20

01

20

02

20

02

20

03

20

03

20

04

20

05

20

05

20

06

20

06

20

07

20

08

20

08

20

09

20

09

20

10

20

10

20

11

20

12

20

12

20

13

20

13

20

14

20

15

20

15

20

16

20

16

20

17

20

17

Year

-on

-yea

r gr

ow

th

CHIP INIP AEIP

22

China Industrial Production Growth

The relationship between copper prices and China’s growth in industrial production is not as clear as might

be expected. CHIP was growing at around 16% between 2004 and 2008, and China’s entry into the global

copper market as a net importer from 2004 appears to have significantly boosted copper prices. CHIP

plunged during the GFC in 2008, and this downturn was reflected in a steep drop in copper prices. CHIP

subsequently recovered in 2009-2010 as the Chinese government initiated a massive fiscal stimulus

package, aimed mainly at infrastructure and residential construction. Copper prices rebounded and even

exceeded their previous levels. Since 2010, CHIP has been on a downward trend, from highs around 16%

to a stable average around 6% since 2015. Copper prices reflect this deceleration in CHIP until 2016, when

they began picking up again. The cross correlogram suggests that Chinese industrial production leads

copper prices by about two months, with a highest correlation coefficient of 0.558. This two-month lead

makes sense, in that a rise in CHIP would likely result first in a decline in copper inventories, and then a

rise in prices signalling excess demand.

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0

4

8

12

16

20

24

28

32

04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS CHIP

23

India Industrial Production Growth

India is the world’s second largest emerging economy and has been growing mostly at high rates over the

past 15 years. It is therefore also expected to have an impact on demand for commodities including base

metals such as copper, although on a smaller scale than China. However, the figure below shows that

there is no clear association between copper prices and India’s industrial production index, aside from the

plunge in 2008 and subsequent recovery. This is further borne out by the cross correlogram, which shows

a negligible positive correlation no matter what the lag length.

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

-15

-10

-5

0

5

10

15

20

25

30

03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS INIP

24

Advanced Economies Industrial Production Growth

Industrial production in the advanced economies has been fairly steady over the past 15 years, with the

major exception of the 2008-2009 Great Recession. For the remainder of the period, there is no clear

evidence of a direct association with copper prices. At the very least, however, AEIP may serve as a proxy

that can capture the effect of the Great Recession. The correlation between CPS and AEIP is 0.51 at zero

lags.

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

-25

-20

-15

-10

-5

0

5

10

15

20

03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS AEIP

25

US dollar index

The figure below plots copper spot prices along with the US dollar index. Clearly, the two series exhibit

similar trends over most of the period 2005 to 2017, suggesting that at least some of the movement in

copper prices can be explained by movements in the USD. The cross correlogram confirms that there is a

reasonably strong correlation coefficient of 0.63 at zero lags, and this damps down at successively higher

lags.

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

11,000

76

80

84

88

92

96

100

104

108

112

05 06 07 08 09 10 11 12 13 14 15 16 17

CPS USD

26

Chilean Peso

As discussed earlier, Chile is the world’s leading copper producer, with a 27% market share in 2016.

Furthermore, copper accounts for about half of Chile’s exports. Therefore, it is expected that the value of

Chile’s currency, the peso, on international markets would (partly) reflect the market’s perceptions of

future movements in copper prices. Indeed, as the chart below shows, there has been a close association

between the USD/peso exchange rate and the spot price of copper. This is further confirmed by the cross

correlogram, which shows that the contemporaneous correlation coefficient for the period 2003 to 2017

is 0.75. However, the highest correlation occurs at a zero lag between the two series, suggesting that

knowledge of today’s peso exchange rate may not help predict future copper prices. Essentially, it could

be that the same information that is available about fundamental drivers of copper prices is incorporated

into the current spot price as well as the peso exchange rate.

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

.0010

.0012

.0014

.0016

.0018

.0020

.0022

.0024

.0026

.0028

03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS CLPESO

27

Oil Price

Crude oil is the most-traded global commodity, and as such it serves as a strong indicator of major global

economic events. It is therefore expected that the prices of oil and other globally traded commodities,

including copper, will tend to track each other fairly closely. Of course, there are some fundamental

drivers that are unique to oil markets, including supply-side issues and geopolitical risks. As can be seen

in the chart below, there has been a strong association between crude and copper prices over the past 15

years. This is confirmed by the correlation coefficient (at zero lags) of 0.83. The cross correlogram suggests

that changes in copper prices might lead changes in oil prices by one month.

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0

20

40

60

80

100

120

140

160

04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS OILP

28

S&P500 Share Price Index

The figure below plots the 12-month log price returns from the S&P500 against copper prices, and

shows that the two series are reasonably closely associated, at least since late 2007. The cross

correlogram shows the contemporaneous correlation coefficient is 0.51, while correlations decline as

the lag length increases. As in the case of other financial variables, therefore, the evidence suggests that

there is limited predictive value in current stock prices for future copper prices.

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

-100

-80

-60

-40

-20

0

20

40

60

80

03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS SP500G

29

Baltic Dry Index

The BDI experienced a massive surge in 2007 and early 2008 during the commodity price super-cycle, but

subsequently crashed during the Global Financial Crisis. Since then, it has fluctuated within a much

narrower band. Although both the spot price of copper and the BDI experienced the effects of the

commodity boom and bust cycle of 2007-2009, overall there is essentially no correlation between the two

series over the period 2003-2017, as confirmed by the cross correlogram.

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

03 04 05 06 07 08 09 10 11 12 13 14 15 16 17

CPS BDI

Summary

Based on the above analysis, it appears that the following variables are likely to provide the greatest

explanatory and forecasting power in structural models: CLPESO, USD, OILP, CHIP, AEIP and SP500G.

30

Model Results The following subsections present the model and forecast results for ARIMA models, a VECM using spot

and futures prices, and structural models, respectively. The fourth subsection provides a comparison of

the various models’ performance in ex post forecasting.

Univariate ARIMA models

The first step in ARIMA modelling is to determine the order of integration of the time series in question.

As shown above in Table 4, the copper spot price series (CPS) contains a unit root. The autocorrelation

function (ACF) of CPS provides further evidence of nonstationarity, in that the autocorrelations are close

to unity at one lag, and decay slowly (Figure 13). In contrast, the ACF of CPS in first differences displays

the typical pattern of a stationary process, and in fact suggests that the differenced series might be white

noise. The Q-statistics test the null hypothesis that the sum of the first ‘n’ autocorrelations are not

significantly different from zero. We fail to reject the null at a 5 per cent significant level up to a lag length

of 10. The ACF is therefore indicating that the CPS series follows a pure unit root process, or possibly an

ARIMA(1,1,0) process.

Figure 13: Autocorrelation and partial autocorrelation functions of copper spot price (CPS) in levels

31

Figure 14: Autocorrelation and partial autocorrelation functions of CPS in first differences

The next step in the ARIMA modelling process is to estimate models according to the patterns observed

in the ACF and PACF. These suggest that the first differences of CPS follows at most an AR(1) process, since

only the first AC exceeds the standard-error band. An ARIMA(1,1,0) process was estimated, and although

the AR term was significant, the coefficient was very small. The model was an extremely poor fit (R2 =

0.02). Estimating a more complex model with two autoregressive and two moving average terms, i.e.

ARIMA(2,1,2), resulted in no significant AR and MA terms.

An alternative modelling approach is to use the EViews ‘automatic’ ARIMA modelling procedure, which

runs many combinations of ARIMA(p,d,q) models and selects the one that minimizes a preselected

information criterion (in this case we use the Schwarz criterion, with maximum AR and MA lags of 4 each).

This procedure selects an ARIMA(0,1,0) model, i.e. the underlying series CPS is differenced once and

regressed on only a constant, with no AR or MA terms. The model suggests that D(CPS) is essentially white

noise. The second best model according to the SBC is an ARIMA(1,1,0), which is also selected by the Akaike

information criterion. The forecasts from the ARIMA(0,1,0) model and the ARIMA(1,1,0) are almost

identical, although with slighter larger forecast errors in the latter case.

Estimating the model on a reduced sample period, beginning in 2010M01 so as to avoid the price swings

induced by the Global Financial Crisis (GFC), resulted in poorer ex post forecasts for the year 2017: the

forecast trends downwards whereas the actual valued trended upwards. Finally, a dummy variable was

included for the GFC, taking on a value of one for the months 2008M09 through 2009M07 (D_GFC) and 0

otherwise. This dummy is significant at the 5% level, and does not substantially change the model, in that

one AR term is significant at the 5% level. The resulting forecast for 2017 is marginally better than that

from the original ARIMA(1,1,0) model.

32

Table 8: Regression output for ARIMA(1,1,0) model

Dependent Variable: D(CPS)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 2003M01 2016M12

Included observations: 168

Convergence achieved after 3 iterations

Coefficient covariance computed using outer product of gradients Variable Coefficient Std. Error t-Statistic Prob. C 41.17062 48.95050 0.841066 0.4015

D_GFC -247.3053 120.2268 -2.056990 0.0413

AR(1) 0.139323 0.057140 2.438263 0.0158

SIGMASQ 241423.5 18090.19 13.34554 0.0000 R-squared 0.036085 Mean dependent var 23.69345

Adjusted R-squared 0.018452 S.D. dependent var 501.9572

S.E. of regression 497.3046 Akaike info criterion 15.27992

Sum squared resid 40559145 Schwarz criterion 15.35430

Log likelihood -1279.513 Hannan-Quinn criter. 15.31011

F-statistic 2.046467 Durbin-Watson stat 2.006838

Prob(F-statistic) 0.109415 Inverted AR Roots .14

4,500

5,000

5,500

6,000

6,500

7,000

7,500

I II III IV I II III IV

2016 2017

Forecast Actual

Actual and Forecast

33

Models based on futures prices Table 9 presents a (contemporaneous) correlation matrix for copper spot and futures prices (futures

prices for 3-month, 15-month and 27-month forward contracts). As can be seen, all of the cross-

correlation coefficients are extremely high, namely 0.97 or higher. These figures confirm the very tight fit

among the four series that is visible in Figure 8.

Table 9: Correlation matrix for copper spot and futures prices

CPS CPF03 CPF15 CPF27 CPS 1.000000 0.999545 0.990456 0.971383

CPF03 0.999545 1.000000 0.993573 0.976287

CPF15 0.990456 0.993573 1.000000 0.994064

CPF27 0.971383 0.976287 0.994064 1.000000

Given the theoretical relationship between futures prices and future spot prices as represented in

equation (3), one could expect that the correlation between spot prices and lagged futures prices would

be even higher. However, in the case of copper prices this result does not obtain. Rather, the closest

correlation between CPS and CPF3 is contemporaneous, not lagged (see Figure 15). The same is true in

the case of CPF15 and CPF27, i.e. the correlations are highest at no lag, and gradually decay as the lag

length increases. The implication of this finding is that copper futures prices may not help to forecast

future spot prices – all the major information is already contained in the current spot prices.

Figure 15 : Cross correlogram between spot and 3-month futures prices

34

Indeed, this turns out to be the case when we regress CPS on CPF03. Although most of the diagnostics

look reasonable (such as a highly significant coefficient for CPF03(-3) and a reasonably high R2 of 0.86),

the Durbin-Watson statistic (0.53) reveals a high degree of autocorrelation in the residuals. This is even

more clearly shown in the graph of the actual, fitted and residuals. Clearly, the actual and fitted values

are out of sync, i.e. the fitted values lag the actual values. This induces serial correlation in the residuals.

If autoregressive terms are added to the model to account for the serial correlation, then CPF03 becomes

insignificant and the AR terms dominate. [The RMSE of the 12-period forecast is 474.4.]

Table 10: Regression output for lagged futures prices

Dependent Variable: CPS

Method: Least Squares

Date: 02/23/18 Time: 08:59

Sample: 2003M01 2016M12

Included observations: 168 Variable Coefficient Std. Error t-Statistic Prob. C 988.3855 196.5508 5.028651 0.0000

CPF03(-3) 0.860891 0.030919 27.84298 0.0000

D_GFC -1001.696 267.6669 -3.742323 0.0003 R-squared 0.830152 Mean dependent var 5980.692



Sum squared resid 1.31E+08 Schwarz criterion 16.49730



Prob(F-statistic) 0.000000

-3,000

-2,000

-1,000

0

1,000

2,000

3,000

0

2,000

4,000

6,000

8,000

10,000

03 04 05 06 07 08 09 10 11 12 13 14 15 16

Residual Actual Fitted

35

Cointegration tests were performed between spot prices (CPS) and each of the three futures prices (using

the contemporaneous futures prices). The results are presented in Table 11. The appropriate lag length

for the test was determined by minimizing the Akaike information criteria for each pair of spot and futures

prices, with a maximum of 6 lags tested in each case, and a minimum of 2 lags selected (so that there is

at least one lagged difference term in the cointegration tests). The sample period is 2003M01 to 2017M12,

and the dummy variable for the 2008 shock is included in the test VAR. An intercept but no time trend is

included in the cointegrating vector and the VAR, but the results (for CPF03 and CPF15) are robust to the

inclusion of the intercept in the cointegrating vector only. The results support a cointegrating relation

between copper spot prices and each of the three futures price series, since in each case the null of no

cointegration is rejected but the null of at most one cointegrating vector is not rejected.

Table 11 : Cointegration tests between spot and futures prices

Trace Test Maximum Eigenvalue Test Lag length

k = 0 k

36

Vector Error Correction Estimates

Date: 02/23/18 Time: 09:21

Sample: 2003M01 2016M12


Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 CPS(-1) 1.000000

CPF03(-1) -0.978622

(0.00765)

[-127.979]

C -157.2530 Error Correction: D(CPS) D(CPF03) CointEq1 -1.315257 -1.175380

(0.54260) (0.53321)

[-2.42397] [-2.20435]

D(CPS(-1)) 1.641331 1.755648

(1.20876) (1.18783)

[ 1.35787] [ 1.47803]

D(CPF03(-1)) -1.510862 -1.632854

(1.23045) (1.20914)

[-1.22790] [-1.35042]

C 37.95822 36.42127

(39.4086) (38.7263)

[ 0.96320] [ 0.94048]

D_GFC -245.6866 -221.9732

(151.394) (148.773)

[-1.62283] [-1.49203] R-squared 0.071877 0.066532

Adj. R-squared 0.049101 0.043625

Sum sq. resids 39053098 37712497

S.E. equation 489.4789 481.0042

F-statistic 3.155806 2.904429

Log likelihood -1276.325 -1273.391

Akaike AIC 15.25387 15.21894

Schwarz SC 15.34684 15.31191

Mean dependent 23.69345 23.66369

S.D. dependent 501.9572 491.8524 Determinant resid covariance (dof adj.) 2.14E+08

Determinant resid covariance 2.01E+08

Log likelihood -2082.949

Akaike information criterion 24.93987

Schwarz criterion 25.16301

Number of coefficients 12

37

Structural models

We employ a general-to-specific modelling strategy, i.e. starting with the most general model that

includes all of the potential explanatory variables. The first step is to estimate an ARDL model, with the

lag length for each dynamic variable chosen according to the Schwarz Criterion (SC), subject to a maximum

of 4 lags. As can be seen in the regression output, the coefficients of CHIP, AEIP, BDI and SP500G are

insignificant even at the 10% level. Therefore, these variables were dropped one at a time, and the model

re-estimated.

Table 12: Regression output for initial ARDL model


Method: ARDL

Sample (adjusted): 2005M01 2017M11

Included observations: 155 after adjustments

Maximum dependent lags: 4 (Automatic selection)

Model selection method: Schwarz criterion (SIC)

Dynamic regressors (4 lags, automatic): CHIP AEIP CLPESO USD OILP

BDI SP500G

Fixed regressors: C

Number of models evalulated: 312500

Selected Model: ARDL(1, 0, 0, 1, 1, 1, 0, 0)

Note: final equation sample is larger than selection sample Variable Coefficient Std. Error t-Statistic Prob.* CPS(-1) 0.885336 0.036256 24.41895 0.0000

CHIP 14.17044 17.71616 0.799860 0.4251

AEIP -5.334533 11.25646 -0.473908 0.6363

CLPESO 2276917. 640735.5 3.553599 0.0005

CLPESO(-1) -1753727. 669534.9 -2.619322 0.0098

USD 68.94486 20.01945 3.443894 0.0008

USD(-1) -79.84120 19.53805 -4.086447 0.0001

OILP 18.12781 6.223907 2.912609 0.0042

OILP(-1) -15.65693 5.778118 -2.709694 0.0076

BDI -0.012941 0.020239 -0.639387 0.5236

SP500G 4.585607 3.378945 1.357112 0.1769

C 516.8669 879.6128 0.587607 0.5577 R-squared 0.945977 Mean dependent var 6554.079






Prob(F-statistic) 0.000000 *Note: p-values and any subsequent tests do not account for model

selection.

38

This process resulted in CHIP and AEIP and BDI being discarded from the model, but SP500G is retained as it has a p-value of 0.06, which is borderline. All of the other variables enter with a contemporaneous term and one lagged term. (The sample period begins in 2005M01 because that is when the USD index series drawn from Bloomberg begins.)

Table 13: Regression output for final ARDL model


Method: ARDL

Date: 03/08/18 Time: 13:47



Maximum dependent lags: 4 (Automatic selection)

Model selection method: Schwarz criterion (SIC)

Dynamic regressors (4 lags, automatic): CLPESO USD OILP SP500G

Fixed regressors: C

Number of models evalulated: 2500

Selected Model: ARDL(1, 1, 1, 1, 0)

Note: final equation sample is larger than selection sample Variable Coefficient Std. Error t-Statistic Prob.* CPS(-1) 0.877392 0.033963 25.83402 0.0000

CLPESO 2436979. 620576.7 3.926959 0.0001

CLPESO(-1) -1764499. 645562.7 -2.733272 0.0070

USD 68.77676 19.18942 3.584097 0.0005

USD(-1) -77.51501 18.79866 -4.123433 0.0001

OILP 17.30869 5.916774 2.925360 0.0040

OILP(-1) -15.74160 5.470440 -2.877575 0.0046

SP500G 4.214525 2.228766 1.890968 0.0606

C 292.3698 537.1813 0.544267 0.5871 R-squared 0.945435 Mean dependent var 6558.264






Prob(F-statistic) 0.000000 *Note: p-values and any subsequent tests do not account for model

selection.

The next step in the ARDL modelling procedure is to test for cointegration among CPS and the selected

explanatory variables, using the bounds test. The results show that the test is inclusive, since the F-statistic

is smaller than the upper bound (thus we cannot reject the null hypothesis of no levels relationship), but

is greater than the 2.5% lower bound (indicating that we cannot conclusively fail to reject the null).

Dropping the marginally significant variable SP500G from the model did not change the result of the test.

Nor did the result change when an unrestricted constant is specified (i.e., the constant does not appear

in the error correction term) instead of a restricted constant (i.e., the constant appears in the error

correction term).

39

F-Bounds Test Null Hypothesis: No levels relationship Test Statistic Value Signif. I(0) I(1)

Asymptotic:

n=1000

F-statistic 3.045368 10% 2.2 3.09

k 4 5% 2.56 3.49

2.5% 2.88 3.87

1% 3.29 4.37

Actual Sample Size 156 Finite Sample:

n=80

10% 2.303 3.22

5% 2.688 3.698

1% 3.602 4.787

A Johansen-type cointegration test was also performed within a VAR(2) model including four I(1) variables,

but excluding the I(0) variable SP500G. The results are mixed, with the Trace test finding one cointegrating

vector at the 5% level and the Maximum Eigenvalue test finding no cointegration. Again, therefore, the

result is inconclusive. However, considering that our primary interest is in constructing a forecast rather

than testing theoretical relationships, we proceed to use the ARDL model for forecasting purposes.



Trend assumption: Linear deterministic trend

Series: CPS CLPESO USD OILP

Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace)

Hypothesized Trace 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * 0.148830 53.61845 47.85613 0.0131

At most 1 0.091846 28.64118 29.79707 0.0675

At most 2 0.065595 13.70829 15.49471 0.0913

At most 3 0.020384 3.192226 3.841466 0.0740 Trace test indicates 1 cointegrating eqn(s) at the 0.05 level

* denotes rejection of the hypothesis at the 0.05 level

**MacKinnon-Haug-Michelis (1999) p-values

Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized Max-Eigen 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None 0.148830 24.97727 27.58434 0.1040

At most 1 0.091846 14.93289 21.13162 0.2936

At most 2 0.065595 10.51607 14.26460 0.1802

At most 3 0.020384 3.192226 3.841466 0.0740

40

Max-eigenvalue test indicates no cointegration at the 0.05 level

* denotes rejection of the hypothesis at the 0.05 level

**MacKinnon-Haug-Michelis (1999) p-values

4,000

4,500

5,000

5,500

6,000

6,500

7,000

7,500

8,000

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

2017

CPS_F_ARDL Actuals ± 2 S.E.

Forecast: CPS_F_ARDL

Actual: CPS

Forecast sample: 2017M01 2017M12


Root Mean Squared Error 514.0704

Mean Absolute Error 396.5811

Mean Abs. Percent Error 5.985965

Theil Inequality Coef. 0.041939

Bias Proportion 0.392168

Variance Proportion 0.538467

Covariance Proportion 0.069364

Theil U2 Coefficient 1.762121

Symmetric MAPE 6.266457

41

Comparison of ex post model forecasts

The figure below plots the 2017 ex post forecasts from four different models. The visual comparison is

confirmed by the measures of forecast performance in Table 14, namely the Root Mean Square Error and

the Mean Absolute Error. It should be noted, however, that the VAR model provides a better short-term

forecast (6 months) than the ARIMA model. The 12-month forecast performance ranked from best to

worst is as follows:

1. VECM with spot and 3-month futures prices [CPS_FVEC];

2. structural ARDL model [CPS_FARDL];

3. ARIMA(1,1,0) [CPS_FAR];

4. VAR based on structural variables [CPS_FVAR].

Figure 16: Comparison of ex post model forecasts for 2017

4,500

5,000

5,500

6,000

6,500

7,000

7,500

I II III IV I II III IV

2016 2017

CPS CPS_FAR CPS_FVEC

CPS_FARDL CPS_FVAR

Table 14: Comparison of forecast errors for 2017

Model RMSE MAE

Univariate: ARIMA(1,1,0) 657.64 545.12

Futures: VECM 412.57 346.94

Structural: ARDL 514.07 396.58

Structural: VAR 749.35 575.25

RMSE = Root Mean Square Error; MAE = Mean Absolute Error

42

Ex ante forecast for 2018

The final step is to use our models to generate ex ante forecasts for 2018. Unfortunately, using the

structural model for ex ante forecasts would require prior forecasts for all of the contemporaneous

explanatory variables (USD, OILP, CHLPESO, SP500). Such an exercise is beyond the scope of the current

paper. However, the other three models can be solved to produce dynamic ex ante forecasts, since in

each case the explanatory variables enter the equations with one or more lags. All three models, i.e. the

ARIMA(1,1,0), the 4-variable VAR and the VECM incorporating 3-month copper futures prices, forecast

that copper prices will continue their upward trend for the remainder of 2018. The VEC predicts the largest

increase (to $8008/tonne in December 2018), followed by the VAR and then the ARIMA model. These

forecasts are consistent with the judgement based on market dynamics that sees demand rising on the

back of faster global economic growth while supply from copper mines is constrained in the short term,

resulting in upward pressure on prices.

Figure 17: Ex ante copper price forecasts for 2018

4000

4500

5000

5500

6000

6500

7000

7500

8000

8500

Jan16

Mär16

Mai16

Jul 16 Sep16

Nov16

Jan17

Mär17

Mai17

Jul 17 Sep17

Nov17

Jan18

Mär18

Mai18

Jul 18 Sep18

Nov18

US$

/to

nn

e

Copper price AR fcst VAR fcst VEC fcst

43

Conclusions In this paper we set out to develop a range of forecasting models for copper spot prices. Three classes of

models were created, namely univariate ARIMA models, bivariate Vector Error Correction Models using

spot and futures price series, and structural models utilising a range of fundamental and financial

explanatory variables (both ARDL and VAR modelling approaches were tested). Preliminary analysis using

graphs and cross-correlograms revealed several notable features of the monthly data series: (1) copper

spot prices appeared to undergo a structural break around 2003/4, coinciding with China's entry into the

global market as a net copper importer, following which the series has exhibited much greater volatility

and a higher average price than previously; (2) the 2008 global financial crisis had a major impact on

copper prices, as well as on many of the explanatory variables considered; (3) spot and futures prices are

contemporaneously correlated, with the gap between them (the "cost of carry") effectively disappearing

following the GFC; (4) unit root tests indicate that copper prices follow a difference stationary (random

walk) process; (5) most of the structural and financial variables also contain unit roots, with the exception

of the series that are in growth rate form, such as industrial production. Given the structural break

mentioned above, it was decided to limit the estimation sample period to 2003M01 to 2016M12; this

allows ex post forecasting over the twelve months of 2017.

An ex post forecast comparison of the four types of models showed that a VECM based on 3-month futures

prices performed best (evidence for cointegration between copper spot and futures prices was found),

followed sequentially by a structural ARDL (incorporating the US dollar index, Chilean peso exchange rate,

oil prices and S&P 500 index), a structural VAR (with the same variables, except S&P500), and finally an

ARIMA(1,1,0) model. Nevertheless, the random walk behaviour of copper prices suggests both that

copper markets are operating efficiently, and that forecasting future prices will remain an arduous task.

Contrary to expectations, Chinese copper imports are not correlated with copper prices, which suggests

that financial factors may be more important than fundamentals as determinants of copper prices in

today's context of financialised commodity markets. The strength or weakness of the US dollar against

other currencies emerged as a key determinant of copper prices.

44

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