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The purpose of this work is to identify variables that are relevant to the copper price setting in the international market. Thus statistical hypothesis tests and statistical tools that help to identify historical relevance and to measure the intensity of the impact of each variable on the copper price on several time horizons were applied. At the end, a regression model that aims to assess the combined effect of the considered time series was estimated. The global industrial production and the aluminum price showed the greatest evidences of being relevant to the copper price. The results suggest that copper stocks, foreign exchange rates and crude oil price should also be considered.

Copper is the industrial metal with the highest financial volume and negotiations in the international commodity markets. Producers, consumers, and financial market players observe the copper market once copper price movements represent a relevant global economy leading indicator. Thus there is a relationship between the copper price and relevant indicators of global economic activity.

Present in the production chain of industrial products, in particular in the electronic industry equipment, the transport sector computer industry, through the automotive vehicles production, the use of copper is very widespread among several sectors and industries, mainly due its durability, machinability and the ability to be molded with high precision and tolerance. It’s thermal conductivity and resistance to extreme environments allows its use in heat exchangers, pressure vessels and tanks. Thus, the demand for copper means the production of items such as wires, rods, tubes, plates and ingots, which will later be used directly in a final application or in the production other goods. Currently, copper is also widely used in technology equipment such as cell phones and computers, and in products commonly found in modern homes, such as washing machines, refrigerators and air conditioners. Copper is traded among the various agents in the market in several states, among others, refined, concentrated, blister and scrap. But the main demand, or the use, of copper for industry is the use of refined copper. And the reference price of copper traded in its various forms is refined copper. It is in this state that copper is traded in the various organized international markets, and the prices practiced in these markets are the benchmarks for establishing prices in refined copper negotiations, and in other states, in the world. The London Metal Exchange (LME) is the most traditional metal trading exchange in the world, with representative daily trading volumes; it is an important reference for the negotiations of metals for the world economy. Also worthy of mention is the Chicago Mercantile Exchange (CME), which is a major exchange for copper trading, and the Shanghai Futures Exchange (SHFE), which has become an important exchange in the global scenario, with growing Chinese participation in the metal markets in general.

As [

This paper aims to identify and evaluate and quantify the relationship between copper price and some of the variables potentially relevant to the process of copper price formation in the international market. Among these variables, global production of refined copper, the crude oil price in the international market, the aluminum price in the international market, the global refined copper stock, the global industrial production variation and the exchange rate can be mentioned. In order to achieve these objectives, econometric procedures were implemented, such as: cointegration tests, causality tests, estimation of impulse response function and linear regression models. These different classical statistical inference methods applied here should enable market makers and other economic agents who participate directly or indirectly in the copper market to better understand the actions or movements in the decision-making related to transactions with copper or copper containing products in its production chain.

In addition to this introduction, this work presents in Section 2 a brief of literature review and details the methodological approach adopted for the development of the research in the Section 3 followed by the presentation of the sample or data used, in Section 4. Section 5 is related to analysis of the results obtained. Finally, Section 6 presents the conclusion and final comments of this work.

Many studies and surveys have been developed to evaluate relevant variables and indicators for copper price formation in the international market. Among these works, some were selected here for a brief review of the literature presented in the following paragraphs.

With information from January 1994 to October 2003, [

Another relevant work related to the topic was presented by [

The [

Another work that deserves attention was developed by [

In order to achieve the objective of this work, the methodology used includes procedures that seek to evaluate, measure and understand the effects of several variables potentially relevant to the copper price in the international market. In this sense, each variable considered important was analyzed and its relations with the price of copper evaluated. For each of these related variables, checks or hypothesis tests are performed which are presented below.

Initially, in order to characterize the time series involved in this work, the stationarity and normality assumptions were verified, respectively, through the Augmented Dickey Fuller and Jarque-Bera tests. Then, through the stationarity evaluation of the residual error of the linear combination of the involved variables, the hypotheses of cointegration between the selected variables and the copper price are verified. The determination of the cointegration between the time series the selected variables and the copper price is important per se for the estimation of autoregressive vector models or VAR models. Moreover, these models are fundamental for the study of the causality of variables and of regression models that represent the causal relationship of the selected variables with the price or variation of the copper price in the international market. Finally, analyzes of the impulse response function were carried out, in order to measure the possible causality verified in several time horizons, since the present study mainly tries to verify the temporal precedence between the variables.

In the tests of the cointegration hypothesis between copper prices and the selected variables, the concept introduced by [_{t} and Y_{t}, for example, the combination that expresses the long term relationship can be obtained by linear regression between the variables, resulting in the following equation:

Z t = β 1 + β 2 X t + e t ⇒ e t = Z t − β 1 − β 2 X t (1)

where X_{t} and Y_{t} are the values of two time series of the variables X and Y at time t, β_{1} and β_{2} are parameters and e_{t} is the residue or stochastic term. If the term e_{t} does not have a unit root, it can be said that the series are cointegrated, removing the possibility of a spurious regression and showing that there is a long-term relationship between the variables. The stationarity test used in this work was the Augmented Dickey Fuller unit root test, or ADF test. The null hypothesis of the Engle-Granger cointegration test states that the series are not cointegrated. In practice, two equations are estimated: in the first X_{t} is estimated as dependent variable and Y_{t} as independent variable, as presented in Equation (1) above; and in the second X_{t} is estimated as dependent variable and Y_{t} as independent variable. If at least one of the two equations the coefficient of the dependent variable is statistically significant then the null hypothesis is rejected, that is, it can be said that the time series X_{t} and Y_{t} are cointegrated.

Autoregressive vector models, or VAR models, are commonly used in interrelated time series prediction systems and to analyze the dynamic impact of random perturbations on the system of variables. These are models in which a variable is explained by its own past value and by past values of the other endogenous variables of the model. In general, as [

Y t = β 1 + β 2 Y t − 1 + β 3 Z t − 1 + ε 1 t (2)

Z t = β 4 + β 5 Z t − 1 + β 6 Y t − 1 + ε 2 t (3)

where the time series X_{t} and Y_{t} are stationary. If this does not occur, the n differences of the variables are used until the differences from these variables become stationary, that is the time series are integrated until they become stationary. After this procedure, these variables are said integrated of order n, or I(n). It is worth noting, however, that the use of large n can generate problems in small samples, since the estimation of the parameters of the VAR model will consume many degrees of freedom, as observed by [

X t = β 1 + β 2 Y t + μ t (4)

where μ_{t} is stationary. Thus, a restricted case of VAR model, called vector model with error correction, or VEC model, consists of the system of equations presented below, in which all variables are stationary, as in the VAR model, and cointegrated. This system can be represented as follows:

Δ X t = α 1 + α 2 μ t − 1 + ε 1 t (5)

Δ Y t = α 3 + α 4 μ t − 1 + ε 2 t (6)

where Δ is the differentiation operator, that is, Δ X t = X t − X t − 1 . By replacing the residual term lagged, this system can be rewritten as follows:

X t = α 1 − ( α 2 β 2 − 1 ) X t − 1 − α 2 β 1 + α 2 Y t − 1 + ε 1 t (7)

Y t = α 3 + ( α 4 + 1 ) Y t − 1 − α 4 β 1 − α 4 β 2 X t − 1 + ε 2 t (8)

In the equations above, α_{2} and α_{4} are the error correction coefficients, since they indicate the magnitude of the response of the variables X_{t} and Y_{t} to a variation in the residual term μ_{t−}_{1}. The coefficients must, in order to guarantee stability, satisfy the following constraints: 0 ≤ α 2 < 1 and − 1 < α 4 ≤ 0 . For a positive stochastic term, for example, ΔX_{t} will be positive and ΔY_{t} will be negative, thus restoring the equilibrium described by cointegration. In addition, the fact that the modules of these parameters are lower than the unit ensures that the model has no explosive behavior. For more details, one can draw on the work of [

As observed in [_{t} and Y_{i}, we are interested in whether there is a precedence relationship between them, or whether they occur simultaneously. This is the essence of Granger’s causality test, which does not seek to identify a causal relationship in its sense of endogeneity. For further detail, one can draw on the work of [_{t} and Y_{i}, the Granger causality test assumes that the relevant information for the prediction of the respective variables X and Y is contained only in the time series on these two variables. Thus, a series of stationary time X causes, in the sense of Granger, another stationary series Y if better statistically significant predictions of Y can be obtained by including lagged values of X to the lagged values of Y. The causality test statistic of Granger is an F test, where the null hypothesis states that there is no causality between the analyzed variables, that is, statistical evidence is required to conclude that there is causality, rejecting the null hypothesis. The test involves the estimation of the following autoregressive vector model:

X t = ∑ i = 1 n β 1 X t − i + ∑ j = 1 n β 2 Y t − j + u 1 t (9)

Y t = ∑ i = 1 n β 3 Y t − i + ∑ j = 1 n β 4 X t − i + u 2 t (10)

Equation (9) postulates that current values of X are related to past values of X itself as well as to lagged values of Y. Equation (10), on the other hand, postulated a similar behavior for the variable Y. Nothing prevents the variables X and Y from being represented in the form of growth rates since the economic or financial variables in general are not stationary in their levels. In this work, the logarithmic returns of the variables selected and analyzed were used. When the variables are cointegrated, the Granger causality test must be carried out in another way, incorporating possible long-term effects into a short-term analysis, which is the essence of cointegration. In this case, the set of equations related to the VEC model is used. The error correction mechanism is intrinsic to VEC models and verifies that lagged values of one variable can help explain the present values of another variable Y, even if past changes of Y are irrelevant. The intuition is that if the two variables are cointegrated, then part of the current change in X can be the result of corrective movements in Y so that the long-term equilibrium with the variable X is again reached. Since X and Y have a common tendency, causality must exist in at least one direction. There will be a causal relationship if the coefficient of error in the previous period, that is, μ_{t−}_{1} is significant and/or if the coefficients of the term of each variable as an explanatory variable of the other are significant. It should be noted that the determination of the number of lags is essential in the study of the causality relation. [

As for the impulse response function, the same as Granger’s causality test indicates that there is a precedence relationship between two variables, it tells us nothing about the intensity of this effect, and how that intensity varies for different time horizons. To meet this need, you can use the impulse response function. [_{t} be a time series described by the following VAR model:

Y t = ρ Y t − 1 + ν t y (10)

where ν t y is the residual term. Assuming zero initial value for this series, the effects on this series of a unitary shock at the initial time can be evaluated without additional shocks. In the specific case where ρ = 1, that is, a unit root process soon non-stationary, there is an “infinite memory” process, in which the effect of the initial shock would never be dissipated. Making an analogy with physics, this situation can be understood as a disturbance on a ball initially at rest on a frictionless table: the ball will be in motion indefinitely. In cases where ρ < 1, the variable will initially feel the effect of the shock, but will return to the null value after a certain period of time. The greater ρ, the longer the time needed to fully dissipate the effect of the initial shock. For the case of bivariate VAR model, we have the following equations:

X t = ∑ i = 1 n α i X t − i + ∑ j = 1 n β j Y t − j + ν t x (11)

Y t = ∑ k = 1 n γ k X t − k + ∑ l = 1 n δ l Y t − l + ν t y (12)

[

Copper is traded in several organized markets around the world and in general, in light of the market efficiency hypothesis their prices are related. And in moments of informational inefficiency these markets offer arbitrage operations opportunities. Thus, in general, price differences between the copper markets usually reflect the cost of transport between these markets and some other differential resulting from local supply and demand. As mentioned earlier, major exchanges for refined copper trading are in London, the London Metal Exchange―LME, in Chicago, the Chicago Mercantile Exchange―CME, and in Shanghai, the Shanghai Futures Exchange―SFE. Among these, LME can be considered the main one, given its tradition and large volume traded daily. Thus the copper price information used in this survey was the copper price traded on the spot market of LME, the price for immediate delivery of the metal that best represents the physical market situation of the metal, collected on the Bloomberg website, beside the monthly copper price traded on the spot market in US$ per ton, the data used in this work were: total monthly production of refined copper, in millions of tons; monthly Brent spot price in US$ per barrel; monthly aluminum spot price, in US$ per ton; monthly observable copper stocks, in thousands of tons; exchange rate index, having as basis 100 the month of January 2009; and the monthly global industrial production.

The level of refined copper production is usually considered one of the most relevant variables for the formation of its price. A very high production can lead to an excess of refined copper in the market, which would generate negative pressures on its price. On the other rand, a very low production can leave the market in deficit and this would cause positive pressures on the copper price. The global production data used in this work was collected in the work [

_{t} time series of were calculated according to the following formula:

Variable Selected | Copper Price | Copper Production | Brent Oil Price | Aluminum Price | Copper Stocks | Exchange Rate | Industrial Production |
---|---|---|---|---|---|---|---|

Mean | 7027.18 | 1706.91 | 87.18 | 1949.10 | 1033.56 | 93.18 | 117.55 |

Median | 7154.24 | 1691.00 | 99.63 | 1928.52 | 1018.01 | 91.05 | 118.99 |

Maximum | 9880.94 | 2024.20 | 124.93 | 2667.42 | 1611.10 | 10919 | 128.57 |

Minimum | 3260.36 | 1395.70 | 37.72 | 1338.06 | 667.13 | 86.94 | 98.76 |

Std Deviation | 1405.02 | 148.38 | 24.73 | 300.82 | 204.08 | 5.60 | 8.45 |

Skewness | −0.4294 | 0.2007 | −0.4977 | 0.2546 | 0.6340 | 1.2572 | −0.6765 |

Kurtosis | 3.2595 | 2.0947 | 1.8655 | 2.7693 | 3.2573 | 3.6610 | 2.5525 |

JB test | 2.7989 | 3.4326 | 7.9728 | 1.0936 | 5.8591 | 23.6552 | 7.1086 |

(p value) | (0.2467) | (0.1797) | (0.0186) | (0.5788) | (0.0534) | (0.0000) | (0.0286) |

ADF | −2.8744 | −1.4158 | −1.1466 | −2.2839 | −2.3318 | −0.6674 | −1.5350 |

(p value) | (0.1762) | (0.8462) | (0.9141) | (0.4377) | (0.4116) | (0.9718) | (0.8137) |

lags | 1 | 24 | 1 | 0 | 12 | 2 | 0 |

Variable Selected | Copper Price | Copper Production | Brent Oil Price | Aluminum Price | Copper Stocks | Exchange Rate | Industrial Production |
---|---|---|---|---|---|---|---|

Mean | 0.0042 | 0.0038 | −0.0021 | 0.0006 | 0.0040 | 0.0011 | 0.0031 |

Median | 0.0035 | 0.0066 | 0.0036 | −0.0078 | −0.0062 | 0.0007 | 0.0028 |

Maximum | 0.1667 | 0.1148 | 0.1866 | 0.1431 | 0.2359 | 0.0277 | 0.0153 |

Minimum | −0.1218 | −0.1089 | −0.2599 | −0.1238 | −0.1361 | −0.0234 | −0.0077 |

Std Deviation | 0.0561 | 0.0399 | 0.0780 | 0.0491 | 0.0720 | 0.0115 | 0.0041 |

Skewness | 0.2533 | −0.0485 | −0.6483 | 0.3277 | 0.3920 | 0.1451 | 0.0954 |

Kurtosis | 3.4570 | 4.0728 | 4.3420 | 3.0256 | 2.9487 | 2.6216 | 3.2202 |

JB test | 1.6096 | 4.0128 | 12.0434 | 1.4875 | 2.1346 | 0.7864 | 0.2936 |

(p value) | (0.4472) | (0.1308) | (0.0024) | (0.4753) | (0.3439) | (0.6749) | (0.8635) |

ADF | −7.3778 | −5.3953 | −7.7961 | −8.6813 | −5.7280 | −7.0027 | −8.8367 |

(p value) | (0.0000) | (0.0001) | (0.0000) | (0.0000) | (0.0000) | (0.0000) | (0.0000) |

lags | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Return X t = ln ( X t X t − 1 ) (13)

The first methodological procedure used in this analysis was the Engle-Granger cointegration test. Since all series of returns are stationary, the use of the Engle-Granger’s cointegration test with these series will erroneously lead to the conclusion that eventually all are cointegrated with the copper price returns time series. Stationary series oscillate over time around an approximately constant mean, that is, it has no tendency and the variance is also approximately constant. The difference between two series with these properties will probably provide a third series with these same properties, thus characterizing, by definition, the existence of cointegration. This means that the Engle-Granger cointegration test must be applied to pairs of non-stationary series. Thus, the original time series not their logarithmic returns were used. The implications of the cointegration tests involving the original time series are also valid for the models that involve the logarithmic returns of these same time series, whose models will consider this relation existing in the context of the original time series. _{t} and the variables selected written as X_{t}.

This analysis is valid for the purpose of an initial evaluation of the results obtained. However, for the following analysis of Granger’s causality an objective decision regarding the existence or non-existence of cointegration is necessary. This is due to the fact that the existence of cointegration requires the development of VEC models, while the lack of it allows the development of VAR models. In this case, the existence of cointegration is usually disregarded for situations in which the pvalue of the Engle-Granger cointegration test is greater than 10%. Assuming the existence of cointegration in a test whose p value is 20%, for example, means accepting a 20% probability that this assumption is wrong, which is a high value. Therefore, for the purposes of the Granger causality test,

Dependent Variable | Copper Price | Variable X_{t} | ||||
---|---|---|---|---|---|---|

Variable X_{t} | ADF Test | (p value) | lags | ADF Test | (p value) | lags |

Copper Prodution | −2.9077 | 0.1452 | 1 | −0.3247 | 0.9745 | 11 |

Brent Price | −2.7422 | 0.1956 | 1 | −1.4526 | 0.7813 | 2 |

Aluminum Price | −2.9082 | 0.1449 | 0 | −2.5790 | 0.2555 | 0 |

Copper Stocks | −2.4427 | 0.3131 | 1 | −2.8681 | 0.1564 | 2 |

Exchange Rate | −2.6980 | 0.2109 | 1 | −0.6989 | 0.9446 | 1 |

Industrial Prodution | −1.9933 | 0.5346 | 1 | −1.0830 | 0.8858 | 4 |

all time series analyzed are considered as non cointegrated to the copper price series. Thus, there is no need to develop VEC models, and it is possible to use simply VAR models.

One of the requirements for the development of VAR models is that the time series involved are stationary. Since all series of logarithmic returns of the selected variables are stationary, they will be used without any problems. An important definition for the development of VAR models is the number of lags of the endogenous variables used. There are methods or criteria for defining the number of these lags, one of which is Akaike’s criterion. However, in order to avoid the risk of disregarding any relevant models not indicated by this criterion, it was decided to develop models with all lags up a 12 months limit. Granger’s causality tests were made for all lags up to this 12 month limit and the one that provided the lowest p value was chosen, that is, the one that presents the most statistical evidence of the existence of causality in the Granger sense. The Granger causality tests results are summarized in

The values highlighted in

Lags | Copper Prodution | Crude Oil Price | Aluminum Price | Copper Inventorie | Exchange Rate | Industrial Prodution |
---|---|---|---|---|---|---|

F (p value) | F (p value) | F (p value) | F (p value) | F (p value) | F (p value) | |

1 | 0.153 (0.696) | 0.100 (0.752) | 0.004 (0.949) | 0.591 (0.444) | 0.885 (0.350) | 0.442 (0.508) |

2 | 0.351 (0.705) | 0.156 (0.856) | 2.337 (0.104) | 0.796 (0.455) | 1.443 (0.243) | 0.847 (0.433) |

3 | 0.065 (0.978) | 0.243 (0.866) | 2.102 (0.107) | 1.000 (0.398) | 1.811 (0.153) | 1.188 (0.321) |

4 | 0.348 (0.844) | 0.498 (0.797) | 2.139 (0.085) | 1.448 (0.227) | 1.106 (0.361) | 1.372 (0.253) |

5 | 0.428 (0.827) | 0.584 (0.712) | 3.373 (0.009) | 1.049 (0.397) | 0.731 (0.603) | 1.196 (0.321) |

6 | 0.393 (0.881) | 0.526 (0.786) | 3.017 (0.012) | 0.995 (0.436) | 1.217 (0.309) | 2.050 (0.072) |

7 | 0.323 (0.941) | 0.325 (0.940) | 2.199 (0.047) | 0.700 (0.672) | 1.201 (0.316) | 2.655 (0.018) |

8 | 0.284 (0.969) | 0.321 (0.955) | 2.247 (0.037) | 0.558 (0.808) | 1.019 (0.432) | 2.561 (0.018) |

9 | 0.312 (0.968) | 0.278 (0.978) | 1.897 (0.072) | 0.446 (0.904) | 1.021 (0.435) | 2.339 (0.026) |

10 | 0.308 (0.976) | 0.594 (0.812) | 1.592 (0.135) | 0.459 (0.909) | 0.959 (0.489) | 2.059 (0.045) |

11 | 0.307 (0.981) | 0.707 (0.726) | 1.615 (0.124) | 0.404 (0.948) | 0.933 (0.517) | 1.920 (0.060) |

12 | 0.259 (0.993) | 0.806 (0.643) | 1.704 (0.097) | 0.352 (0.973) | 0.995 (0.468) | 1.817 (0.074) |

a monthly data, a response time considerably less than one month is not properly captured. The fact that the p values of the models with lower lags, 1 and 2 months, are considerably lower than all others, even if they are still quite high, reinforces this hypothesis that the response time of copper price to production is small. Another possibility is that copper production does not present a temporal precedence relation with the price of the metal. Some analysts argue that it is the demand that is a driver for metal prices, not supply, the offer reacts according to the price and not the other way around. In order to evaluate the reasonableness of this assertion, the VAR model whose dependent variable is copper production was analysed. Here lags of up to 18 months were considered, since the reaction time of producers at the price is expected to be higher. The result obtained reinforces this second hypothesis.

This 8 month period seems insufficient to indicate the time between the decision to invest in a new mine and the first copper extraction. However, it may be the period of time necessary for producers to raise their level of production by investing in improvements in the production process, that is, efficiency gains, increased working hours at the plant, increased capacity utilization and resumption of production in demining mines.

Regarding crude oil, the Brent price also showed no evidence that Granger cause the copper price. The expectation was that this causal relationship existed through production costs: when crude oil price rises, copper production costs rise and thus there would be a pass-through of this rise in costs to the final price. This transmission of the elevation of production cost to the final price is common in markets in which there is product differentiation. In the case of copper, the final price is given internationally as a mirror of the balance between supply

and demand, that is, the producer has little or no influence on the price. Thus, a possible explanation for the absence of causality between crude oil and copper prices is that this transmission is not necessary or not possible: producers may try to pass on changes in their costs to the final price, but they can not because what determines the commodity price are the dynamics of supply and demand.

As for aluminum, Granger’s causal relationship was identified for several lags, the most notable being that at 5 months. This temporal analysis will be evaluated in greater detail later, in the impulse response analysis. At this point, we can see that evidence of Granger’s causal relationship between aluminum and copper prices is very strong: p value less than 1%.

In relation to stocks, the model that presented the best result was the one with 4 months lag. In this model, a p value of 22.7% was verified, which is a value that indicates that the relation with the copper price is not negligible, but it is also not enough for the study to demonstrate with confidence that such a relationship exists. This suggests that the data used is not fully representative of global stocks. In fact, the ICSG estimates copper stocks on the London Metal Exchange (LME), Chicago Mercantile Exchange (CME), Shanghai Futures Exchange (SHFE) and bonded Chinese warehouses to consist of approximately 60% of global copper stocks. The difficulty in accessing stocks outside these locations obfuscates the analysis of this variable.

Granger’s causality of the exchange rate presented a p value of 15.3% for the 3 month lag model. Similar to the case of stocks, this value indicates that there is evidence that there is a causal relationship between the exchange rate and the copper price, although not strong enough for this to be safely stated p values up to 10%. This result alone does not detract from Granger’s causal relationship, however, it is valid to conclude that the inclusion of other relevant currencies in the exchange rate could possibly result in the greater acceptance of Granger’s causality. It is noteworthy to observe that the construction of this simple exchange rate, containing only 4 coins with equal weights, presented a result of such relevance.

Finally, industrial production presented strong evidence that Granger cause copper prices, with a value of 1.8% for the VAR model with a 7 month delay. This relationship was widely expected since industrial production is a good proxy for copper demand.

The interpretation of these VAR models is facilitated and complemented by impulse response function analysis. While Granger’s causality analysis only indicates whether or not there is a precedence relationship between the various variables under analysis and copper price, the impulse response function analysis allows one to measure the intensity of the impact of one variable on the other, and how this intensity varies over time.

For all the variables under analysis, a period of 12 months was considered. In impulse response function plots, the solid blue line indicates the estimated impact on each time period, while dotted red lines consist of a standard deviation above and below this value. In general, the existence of the estimated impact in each period is accepted when the interval between the red dotted lines does not contain the zero line, that is, when the existence of that impact is accepted for variations of up to one deviation for each side. The value of each point represents the impact, in logarithmic return units, on the response variable in all cases, copper price caused by a change of one unit in the return of the impulse variable. In addition the plots show that the period t corresponds to a lag 1 of t − 1, this is because the instant named 1 in the plot corresponds in reality to the instant 0. Therefore the plots contain 13 points not 12.

Starting with copper production,

The impulse response function of the Brent price on the copper price, however, provided a different result than the one suggested by Granger’s causality analysis. While the causality analysis suggested that there is no relevant relationship, the impulse response function plot indicates that there is a positive impact on the copper price with a 10 month lag, as in

in the logarithmic return of the copper price.

Regarding the aluminum price, the analysis of the impulse response function indicates that there is a statistically significant impact on copper price after 5 months, which is in agreement with the result of the Granger causality analysis. However,

some similar applications, they are not perfect substitutes. An example of this is the energy grid: although both metals are used in their construction, each one is more advantageous for a certain application: UHV (ultrahigh voltage) transmission lines are aluminum intensive, while copper is more used in networks of distribution. Thus, positive changes in aluminum price would suggest, in this case, that energy grid investment is more focused on UHV transmission lines and, consequently, less focused on distribution networks. This would imply a lower demand for copper in the period ahead, which would exert negative pressure on its prices. Thus, positive changes in aluminum price would suggest, in this case, that energy grid investment is more focused on UHV transmission lines and, consequently, less focused on distribution networks. This would imply a lower demand for copper in the period ahead, which would exert negative pressure on its prices. Thus positive changes in aluminum price would suggest, in this case, that enegy grid investment is more focused on UHV transmission lines and, consequently, less focused on distribution networks. This would imply a lower demand for copper in the period ahead, which would exert negative pressure on its prices. It is also worth noting that the impulse response function analysis and the previously estimated VAR model agree that this negative effect of aluminum price on copper price after 5 months is approximately −0.5, that is, a positive change in one unit in the return of the aluminum subsequently generates a negative variation of −0.5 in the copper return. However, the VAR model suggests that there are also relevant impacts with other lags; still, the 5 month lag demostrated to be the most relevant.

In relation to stocks, the analysis of the impulse response function presents results similar to those of the Granger causality tests, that is, that there is no statistically significant impact on copper price as shown in

and 3 months, the most relevant being lag of 3 months. Its effect is negative, as expected: a positive change in a stock return unit has a negative impact of −0.39 unit on copper price.

As in the Granger causality test, the impulse response function analysis suggests that there is no relevant impact of the exchange rate on copper price for the level of significance adopted, as shown in

Finally the analysis of the impulse response function for industrial production resembles that of the Granger causality test, when the impact of greater relevance on copper prices occurs with 7 months of lag, as shown in

The previously performed analyzes indicated which variables are individually relevant for the formation of copper price, in what time horizon and with what intensity. It is interesting to evaluate how all the relevant variables identified jointly influence copper price. Relationships found between pairs of variables are possibly lost or altered when doing a global analysis involving several of them simultaneously. For this purpose, a multiple regression model was developed in which copper price is the dependent variable and the variables identified as relevant in the previous analyzes are the explanatory variables. In addition to allowing the joint effect of the relevant variables to be evaluated, the multiple linear regression model allows the determination of how much copper price is explained by these variables through a determination coefficient.

The starting point of the regression model was the results obtained previously in the analysis of the estimated VAR models. The first or preliminary estimated model considers the variables identified as relevant in the developed VAR models, that is, those that presented p value lower or very close to 10%, totaling 20 variables.

Thus, since the greatest interest lies in identifying the relevant variables, this model was modified so as to consider only statistically relevant variables, according to the criterion of p value lower or close to 10%. The procedure adopted consisted in performing successive regressions, always removing the variable

Preliminary Model | Final Model | ||
---|---|---|---|

R-squared | 0.4292 | R-squared | 0.3705 |

Adjusted R-squared | 0.2009 | Adjusted R-squared | 0.2656 |

S.E. of Regression | 0.0497 | S.E. of Regression | 0.0477 |

Sum Squared Resid | 0.1236 | Sum Squared Resid | 0.1363 |

Akaike Criterion | −2.9237 | Akaike Criterion | −3.1075 |

Schwarz Criterion | − 2.6576 | Schwarz Criterion | − 2.7570 |

Paremeter | Estimate | Std Deviation | Stat t | p value | |||
---|---|---|---|---|---|---|---|

1 | Constant term_{ } | −0.0224 | 0.0131 | −1.7116 | 0.0932 | ||

2 | Brent Price_{t−}_{5 } | −0.0835 | 0.1110 | −0,7520 | 0.4556 | ||

3 | Brent Price_{t−}_{10} | −0.0577 | 0.0997 | −0.5786 | 0,5655 | ||

4 | Aluminum Price_{t−}_{1} | −0.4527 | 0.2373 | −1.9081 | 0.0621 | ||

5 | Aluminum Price_{t−}_{3} | −0.0189 | 0.2203 | −0.0858 | 0.9320 | ||

6 | Aluminum Price_{t−}_{5} | 0.0588 | 0.2283 | 0.2575 | 0.7978 | ||

7 | Aluminum Price_{t−}_{6} | 0.3940 | 0.2173 | 1.8132 | 0.0758 | ||

8 | Aluminum Price_{t−}_{7} | 0.3181 | 0.2102 | 1.5131 | 0.1365 | ||

9 | Aluminum Price_{t−}_{11 } | −0.5007 | 0.2162 | −2.3161 | 0.0247 | ||

10 | Stocks_{t−}_{2 } | 0.1337 | 0.1354 | 0.9877 | 0.3280 | ||

11 | Stocks_{t−}_{3} | 0.0257 | 0.1284 | 0.2002 | 0.8412 | ||

12 | Industrial Production_{t−}_{4 } | 3.4682 | 2.2335 | 1.5528 | 0.1268 | ||

13 | Industrial Production_{t−}_{5} | 2.8223 | 2.0033 | 1.4088 | 0.1651 | ||

14 | Industrial Production_{t−}_{6 } | 1.2735 | 1.9425 | 0.6556 | 0.5151 | ||

15 | Industrial Production_{t−}_{7 } | 1.7080 | 1.9394 | 0.8807 | 0.3827 | ||

16 | Copper Price_{t−}_{1 } | −0.4829 | 0.1939 | −2.4905 | 0.0161 | ||

17 | Copper Price_{t−}_{3} | −0.1927 | 0.2230 | −0.8640 | 0.3917 | ||

18 | Copper Price_{t−}_{5 } | 0.1588 | 0.2253 | 0.7048 | 0.4842 | ||

19 | Copper Price_{t−}_{6} | −0.6923 | 0.2203 | −3.1423 | 0.0028 | ||

20 | Copper Price_{t−}_{7 } | −0.0435 | 0.2102 | −0.2069 | 0.8370 | ||

21 | Copper Price_{t−}_{11} | 0.3554 | 0.2298 | 1.5463 | 0.1283 | ||

with higher pvalue with each new or final regression model, until the first or preliminary model was reached in which all the variables met the stipulated criterion. The

Paremeter | Estimate | Std Deviation | Stat t | p value | |
---|---|---|---|---|---|

1 | Constant term_{ } | −0.0219 | 0.0098 | −2.2385 | 0.0289 |

2 | Aluminum Price_{t−}_{1} | −0.4501 | 0.1995 | −2.2557 | 0.0277 |

3 | Aluminum Price_{t−}_{1} | 0.2871 | 0.1799 | 1,5960 | 0.1157 |

4 | Aluminum Price_{t−}_{1} | 0.2393 | 0.1262 | 1.8955 | 0.0628 |

5 | Aluminum Price_{t−}_{1} | −0.2823 | 0.1454 | −1.9418 | 0.0569 |

6 | Stocks_{t−}_{2} | 0.1453 | 0.0853 | 1.7028 | 0.0938 |

7 | Industrial Production_{t−}_{4 } | 4.6688 | 1.9709 | 2.3689 | 0.0211 |

8 | Industrial Production_{t−}_{5} | 4.3138 | 1.5117 | 2.8536 | 0.0059 |

9 | Copper Price_{t−}_{1} | 0.5160 | 0.1715 | 3.0085 | 0.0038 |

10 | Copper Price_{t−}_{3 } | −0.2254 | 0.1321 | −1.7065 | 0.0931 |

11 | Copper Price_{t−}_{6} | −0.5302 | 0.1869 | −2.8372 | 0.0062 |

explanatory power of the model, adjusted for the quantity of inputs, improved. The other measures of model evaluation also indicate that the final model is better than the first one: the standard error was reduced and the Akaike and Schwarz criteria. The exception was due to the sum of square residuals which increased. This, however, was expected since the reduction of R² necessarily implies that there was an increase in the sum of square residues. That is, both should be understood as one criterion. These results suggest that, in fact, the last estimated model or the final model should be maintained.

Analyzing the final regression model obtained, it is worth noting that industrial production is the variable with the greatest impact on copper price as the extremely high level of its coefficients was obtained. This result is consistent with all the previous analyzes, which indicate that industrial production has a strong positive impact on copper prices with a few months of lag. More than that, industrial production coefficients that are much larger than all others suggest that it is the predominant variable that “dictates” the copper price movements while the performance of the others functions as “adjustment”, that is, softening or amplifying movements fundamentally generated in response to industrial production. One thing that reinforces this analysis is the fact that industrial production has shown consistency in terms of its relevance in all the various analyzes. The analysis of the aggregate variables, through the regression model, did not alter the relations observed in the analyzes conducted individually with the industrial production. The same can not be said for the other variables. The Brent oil price, for example, was relevant in the developed VAR model and the impulse response function analysis, however it was discarded in the regression model. On the other hand, the aluminum price was also relevant in all analyzes, but the estimate of its impact varied significantly among them. Signals of the parameters estimates of the VAR model, for example, were reversed in the regression model, indicating an effect opposite to that previously suggested. That is, the inclusion of variables makes the measurement of the effects of aluminum price on copper price more “nebulous”, different from that of industrial production. In any case, it should be noted that aluminum price was considered relevant in all analyzes. The lagged copper price itself was also relevant in the regression model.

It is noteworth to mention that this work is not intend to the discuss about violation of basic assumptions of the linear regression models or robustness of the models, which can be the subject of extensions to this work. Thus the normality is the only basic assumption that was mentioned. Furthermore, it is important to observe that the all results presented in this section was obtained using the econometric software EViews.

The main objective of this work was to identify variables relevant to the formation of copper prices in the international market. Thus, candidate variables were selected and several tests and analyzes were carried out in order to verify the existence of relevance or statistical significance of each of these variables. In order to achieve the objectives of this work, we performed cointegration tests, constructed autoregressive vector models, analyzed impulse response functions and estimated linear regression models. Among the relevant variables for the international copper price, industrial production was the most relevant variable, presenting evidence in all the tests carried out that its impact on the copper price is significant. The aluminum price and the lagged copper itself were also relevant in the various analyzes carried out, although their respective impacts are much weaker and more irregular than the global industrial production. The variables stock, crude oil price and exchange rate were relevant in some analyzes, but in others this did not occur. Thus, it is not possible to say with certainty that these variables are determinant in the copper price, although they should not be discarded in other analyzes or future research. Given the hypotheses verified, the copper production variable did not present any evidence to infer that this variable is relevant for the pricing of copper in the international market.

It should be noted that the results obtained here are linked to the sample used and therefore the time series of the stock and exchange rate variables, which were obtained with limitations, have results that should be viewed with caveats. Regarding the copper production variable, the result obtained indicates that this variable is caused by the price while the reciprocal does not happen. Although this research did not have the main purpose of constructing a regression model to explain the copper price, the estimated model presented a result regarding the direction of copper price variation that deserves to be highlighted: the model showed the direction of the movement in copper prices in 73% of cases. This result can be very useful for market participants, for example in the decision making process of hedge strategies by producers and in the determination of speculative operations with copper prices. The statistical significance of the estimated parameters of the model and the low coefficient of determination obtained indicate that, although relevant, the variables selected are not able to fully explain the fluctuations in copper price. This suggests the existence of other variables not considered in this work that are also relevant for determining the copper price in the international market. Thus other variables can be considered in future work on the theme, such as interest rates, level of scrap use, stock exchange performance and inflation rates.

The results obtained in this work can be used as a basis for the development of other studies that seek to study copper price behavior and its perspectives. In addition to verifying if other variables are relevant for copper pricing, other methodologies and samples that may contribute to the clarification of the topic discussed here should be verified in future works.

The authors declare no conflicts of interest regarding the publication of this paper.

de Salles, A.A., Magrath, R.S. and Malheiros, M.M. (2019) Determination of Copper Price Expectations in the International Market: Some Important Variables. Open Journal of Business and Management, 7, 348-373. https://doi.org/10.4236/ojbm.2019.72024