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Dynamics Behind Cycles and Co-movements in Metal Prices: An Empirical Study Using Band-Pass Filters

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Abstract

After living one of the most intense metal price cycles, several ongoing macroeconomic phenomena with the potential of structurally redefining the long-run supply and demand for metals, and raising divergency regarding where the metal prices are trending, it is suitable to evaluate the dynamics in the metal prices, especially focus on the long cyclical components. This article studies in detail the cyclical components of the real prices of base metals, iron ore, and gold, applying band-pass filters and a novel decomposition over time series with length as far as 1800. The main findings are: (1) the long cyclical components in real prices are highly correlated among them and with the proposed long economic cycles, (2) short and medium cyclical components are more relevant in explaining the price deviations from their trend, but the long cyclical component is not negligible, (3) co-movement in base metals is strong for all the cyclical components, but decreasing as cyclical frequency increases, and (4) prices are either sideways or upward-trending depending on the assumptions for correction of the US Consumer Price Index, which suggests that the supply side of these industries, in the best case, only offset the cost increases by depletion.

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Notes

  1. Composed by the six base metals and iron ore.

  2. The long cycles were argued by various investigators (e.g., van Gelderen 1913; Moore 1914; Layton 1922; Trotsky 1923; and de Wolff 1924).

  3. Christiano and Fitzgerald (2003) demonstrated that the superiority of the ACF is more evident when extracting frequencies lower than the business cycles, i.e., 2–8 years.

  4. Considering a balanced sample.

  5. Approach used by Cuddington and Jerrett (2008).

  6. The models tested, assuming the presence of stochastic trend in the real prices, is

    \(d\ln \left( {CPI - {\text{Adjusted }}\,{\text{Real}}\,{\text{Price}}_{t} } \right) = \beta + u_{t}\) for the actual time series case and

    \(d\ln \left( {CPI\,{\text{Adjusted}}\,{\text{Trend}}\,{\text{Component}}_{t} } \right) = \beta + u_{t}\) for the trend component resulted obtained by the ACF; d refers to the first difference. For details, see Cuddington (2010).

  7. The US’s Consumer Price Index is used as the deflator.

  8. The selection of the lead/lag factor obeys to a trade-off between a better adjustment to the ideal band-pass filter (or reduction of leakage/compression/exacerbation errors near the cutoff frequencies) and the length of available data. K values greater of 11 are known to provide a good fit. However, a value of 45 provided a better fit to the ideal filter given the low band frequency of interest in this research.

  9. A value of 25 was enough to provide a good fit to the ideal band-pass filter.

  10. A value of 25 was enough to provide a good fit to the ideal band-pass filter.

  11. Although the asymmetric method does not ensure that there is no phase change, under conditions such as random walk, its impact is minimal and with significant gains in relation to minimizing the difference with the ideal band-pass filter.

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Acknowledgment

The authors thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for supporting this research (Fund Number: 236482).

Author information

Authors and Affiliations

  1. Department of Mining and Materials Engineering, McGill University, Adams Building, Room 119, 3450 University Street, Montreal, QC, H3A 0E8, Canada

    Matias Marañon & Mustafa Kumral

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  1. Matias Marañon
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Correspondence to Mustafa Kumral.

Appendices

Appendix 1: The Band-Pass Filter and The Christiano–Fitzgerald’s Optimal Approximation

Depending on whether the interest is on low, high or a band of frequency components, as well as the data-generating process, econometricians developed different optimal approximations to the ideal filter, such as the Hodrick–Prescott (HP), Trigonometric Regression Filters, Baxter–King (BK), and Christiano–Fitzgerald (CF).

This article uses the Christiano–Fitzgerald’s optimal “linear” approximation for the asymmetric full sample filter assuming processes I(1) (drift adjusted). It must be acknowledged, though, that the debate on whether commodity prices behave as random walk (RW) process remains open. Briefly, the benefits of the CF band-pass filter, more specifically the CF asymmetric full sample filter (ACF), are:

  1. 1.

    Allows for decomposing the time series in components that fluctuate within a frequency range, for this study, high frequencies (short cycles), medium frequencies (medium cycles), low frequencies (long cycles) and trend.

  2. 2.

    Allows for considering the full data in the estimation of the filter coefficients, unlike the fixed length symmetric options, such as the BK.

  3. 3.

    Has greater adjustment to the ideal band-pass filter at low frequencies (the main focus of interest in this article) in comparison with the BK.

  4. 4.

    Fulfills the desired requirements in a band-pass filter: minimizes the difference with the ideal filter, extracts the desired frequencies without compromising the remnant, minimizes the introduction of phase shiftFootnote 11 and eliminates stochastic trends in the filtered series.

For a closer look at the optimization process followed by Christiano and Fitzgerald, see Christiano and Fitzgerald (2003).

Appendix 2: Test the Random Walk Hypothesis

As the implementation of an ADF without considering structural breaks leads to a bias toward the non-rejection of the null hypothesis (Perron 1989), the analysis of the RWH is complemented with the VRT. This has gained popularity in recent years as a complement to test the hypothesis of weak-form efficiency (Charles and Darné 2009), although it is not without weaknesses as Kim and Kim (2010) pointed out.

Considering a joint interpretation of the results of the ADF test and VRT (Table 14), there is statistical evidence to consider the series as integrated of order 1.

Table 14 Augmented Dickey–Fuller and variance ratio tests
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Appendix 3: Real Prices, Cyclical Components and Trends

See Figures 12, 13, 14, 15, 16, 17, 18 and 19.

Figure 12
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Real Copper price and its cyclical components and trend (log scale)

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Figure 13
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Nickel real price and its cyclical components and trend (log scale)

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Figure 14
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Zinc real price and its cyclical components and trend (log scale)

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Figure 15
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Lead real price and its cyclical components and trend (log scale)

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Figure 16
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Tin real price and its cyclical components and trend (log scale)

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Figure 17
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Aluminum real price and its cyclical components and trend (log scale)

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Figure 18
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Real gold price and its cyclical components and trend (log scale)

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Figure 19
figure 19

Iron ore real price and its cyclical components and trend (log scale)

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Appendix 4: Contrast between the ACF and BK Cyclical Components

See Figures 20, 21, 22, 23, 24, 25, 26, 27 and 28.

Figure 20
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Aluminum, copper, and lead long cyclical components (log scale)

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Figure 21
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Tin, iron ore, and gold long cyclical components (log scale)

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Figure 22
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Nickel and zinc long cyclical components (log scale)

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Figure 23
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Aluminum, copper, and nickel medium cyclical components (log scale)

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Figure 24
figure 24

Zinc, lead, and tin medium cyclical components (log scale)

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Figure 25
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Iron ore and gold medium cyclical components (log scale)

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Figure 26
figure 26

Aluminum, copper, and nickel short cyclical components (log scale)

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Figure 27
figure 27

Zinc, lead, and tin short cyclical components (log scale)

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Figure 28
figure 28

Iron ore and gold short cyclical components (log scale)

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Appendix 5: Evaluation of the Statistical Significance of the Stochastic Trend

See Tables 15, 16, 17, 18, 19, 20, 21 and 22.

Table 15 Trend statistical significance evaluation for the copper price
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Table 16 Trend statistical significance evaluation for the nickel price
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Table 17 Trend statistical significance evaluation for the zinc price
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Table 18 Trend statistical significance evaluation for the lead price
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Table 19 Trend statistical significance evaluation for the tin price
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Table 20 Trend statistical significance evaluation for the aluminum price
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Table 21 Trend statistical significance evaluation for the iron ore price
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Table 22 Trend statistical significance evaluation for the gold price
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Marañon, M., Kumral, M. Dynamics Behind Cycles and Co-movements in Metal Prices: An Empirical Study Using Band-Pass Filters. Nat Resour Res 29, 1487–1519 (2020). https://doi.org/10.1007/s11053-019-09535-z

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