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)
0
5
10
15
20
25
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Mill
ion
to
nn
es
Mine Production Refined Production Refined Usage
18%
1%
69%
2%10% 0%
Europe Africa Asia Latin America North America Oceana
9
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$9,869 per tonne in February 2011.
This surge was driven partly by the cyclical recovery in economies and asset markets following
unprecedented and coordinated intervention by monetary authorities in the major economies. In
addition, the strong price recovery was fuelled by a rapid rise in Chinese demand, propelled by the
country’s massive fiscal stimulus package, which centred on infrastructure investment and construction –
both of which are copper intensive. For the next few years, the price of copper gradually receded as the
Chinese economy's rate of growth decelerated. This price decline continued until January 2016, after
which time the copper price has gradually risen again as Chinese and global demand has picked up steam.
As shown later in the report, fluctuations in the value of the US dollar against other currencies has also
played a significant role in movements in copper prices over the past 15 years.
Figure 7: Copper price and base metals price index
Source: World Bank
As described above, Chinese demand has had a major influence on global copper prices over the past 15
years. With China still consuming about half of the world’s supply, it will likely continue to be the main
price driver for the foreseeable future, aside from possible financial shocks. Structural forecasting models
therefore need to take Chinese demand into account. Other large emerging economies, such as India and
Indonesia, are also becoming increasingly important sources of copper demand.
1 Cheng and Xiong (2014) argue that risk sharing and information discovery provided two economic mechanisms through which financialisation affected commodities markets.
0
20
40
60
80
100
120
140
0
2'000
4'000
6'000
8'000
10'000
12'000
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 20152
01
0 =
10
0
US$
/to
nn
e
Copper price Metals price index
11
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
-200
0
200
400
600
800
1,000
1,200
0
1
2
3
4
5
6
7
03 04 05 06 07 08 09 10 11 12 13 14 15 16 17
SPREAD15 USFFR
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
CPF15 Copper 15-month futures price USD per tonne
CPF27 Copper 27-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
first difference -11.57*
[0.00]
0 -11.60*
[0.00]
2
Futures (15-month) -2.02
[0.28]
0 -2.18
[0.22]
5
first difference -11.70*
[0.00]
0 -11.77*
[0.00]
3
Futures (27-month) -1.19
[0.33]
0 -2.04
[0.27]
5
first difference -12.06*
[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
Adjusted R-squared 0.828093 S.D. dependent var 2150.317
S.E. of regression 891.5580 Akaike info criterion 16.44151
Sum squared resid 1.31E+08 Schwarz criterion 16.49730
Log likelihood -1378.087 Hannan-Quinn criter. 16.46415
F-statistic 403.2270 Durbin-Watson stat 0.536623
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
Included observations: 168
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
Dependent Variable: CPS
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
Adjusted R-squared 0.941821 S.D. dependent var 1617.801
S.E. of regression 390.2192 Akaike info criterion 14.84555
Sum squared resid 21774758 Schwarz criterion 15.08117
Log likelihood -1138.530 Hannan-Quinn criter. 14.94126
F-statistic 227.6362 Durbin-Watson stat 2.024375
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
Dependent Variable: CPS
Method: ARDL
Date: 03/08/18 Time: 13:47
Sample (adjusted): 2005M01 2017M12
Included observations: 156 after adjustments
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
Adjusted R-squared 0.942466 S.D. dependent var 1613.421
S.E. of regression 386.9999 Akaike info criterion 14.81069
Sum squared resid 22016034 Schwarz criterion 14.98664
Log likelihood -1146.234 Hannan-Quinn criter. 14.88215
F-statistic 318.3810 Durbin-Watson stat 2.003381
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.
Sample (adjusted): 2005M02 2017M12
Included observations: 155 after adjustments
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
Included observations: 12
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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