Abstract
In the minerals industry, inadequately addressing technical, economic, social, environmental, and geological uncertainties can lead to poor decisions and unexpected outcomes, such as financial losses, accidents, and liabilities. Correlation analysis is widely used in minerals-related research to estimate variables, but erroneous inferences can be made about causal relationships between variables, leading to higher risk, for example, relationships between discount rate and commodity price, interest rate and inflation, energy costs and gold price, vibration and component wear in mining equipment, and abrasive mineral characteristics and drill bit wear. Therefore, mine valuation and risk analysis in the minerals industry require a strong understanding of the nature of associations between variables. The present paper demonstrates how causality could be used in the mining industry. Four tests were implemented and compared through two case studies. The cointegration test revealed the presence of a long-term connection between cointegrated variables. The Granger, variable-lag Granger, and Toda-Yamamoto causality tests analyzed the nature, lag, and direction of causal relationships between variables. Due to its dynamic time-warping algorithm, the variable-lag Granger causality test showed a robust causal association without any attachments to the possible lag or direction. Two case studies showed that causality tests best facilitate decision-making in the minerals industry by improving understanding of associations between variables.
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The data are used in Case Study 1 are public and available on many websites. The dataset used in Case Study 2 cannot be shared due to confidentiality.
References
Akaike H (1973) Maximum likelihood identification of gaussian autoregressive moving average models. Biometrika 60(2):255–265. https://doi.org/10.1093/biomet/60.2.255
Amornbunchornvej C, Zheleva E, Berger-Wolf T (2019) Variable-lag granger causality for time series analysis. 2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA), pp 21–30. https://doi.org/10.1109/DSAA.2019.00016
Bahmani-Oskooee M, Sohrabian A (1992) Stock prices and the effective exchange rate of the dollar. Appl Econ 24(4):459–464. https://doi.org/10.1080/00036849200000020
Batten JA, Ciner C, Lucey BM (2010) The macroeconomic determinants of volatility in precious metals markets. Resour Policy 35(2):65–71. https://doi.org/10.1016/j.resourpol.2009.12.002
Bruns SB, Stern DI (2019) Lag length selection and p-hacking in Granger causality testing: prevalence and performance of meta-regression models. Empirical Economics 56:797–830. https://doi.org/10.1007/s00181-018-1446-3
Cartwright PA, Kamerschen DR, Huang M-Y (1989) Price correlation and granger causality tests for market definition. Rev Ind Organ 4:79–98. https://doi.org/10.1007/BF02284670
Cheung Y-W, Lai KS (1993) Finite-sample sizes of Johansen’s likelihood ratio tests for cointegration. Oxf Bull Econ Stat 55(3):313. https://doi.org/10.1111/j.1468-0084.1993.mp55003003.x
Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74(366a):427–431. https://doi.org/10.1080/01621459.1979.10482531
Dudda TL, Klein T, Nguyen DK, Walther T (2022) Common drivers of commodity futures? Queen’s Management School Working Paper, 05. https://doi.org/10.2139/ssrn.4231994
Engle RF, Granger CW (1987) Co-integration and error correction: representation, estimation, and testing. Econometrica: Journal of the Econometric Society 251–276. https://doi.org/10.2307/1913236
Gao X, Huang S, Sun X, Hao X, An F (2018) Modelling cointegration and Granger causality network to detect long-term equilibrium and diffusion paths in the financial system. Royal Soc Open Sci 5(3):172092. https://doi.org/10.1098/rsos.172092
Gorton G, Rouwenhorst KG (2006) Facts and fantasies about commodity futures. Financ Anal J 62(2):47–68. https://doi.org/10.2469/faj.v62.n2.4083
Granger CW (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica: J Econ Soc 37:424–438. https://doi.org/10.2307/1912791
Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J Roy Stat Soc: Ser B (methodol) 41(2):190–195. https://doi.org/10.1111/j.2517-6161.1979.tb01072.x
Hoover KD (2001) Causality in macroeconomics. Cambridge University Press. https://doi.org/10.1007/BF02747266
Jerrett D, Cuddington JT (2008) Broadening the statistical search for metal price super cycles to steel and related metals. Resour Policy 33(4):188–195. https://doi.org/10.1016/j.resourpol.2008.08.001
Johansen S (1988) Statistical analysis of cointegration vectors. J economic Dyn Control 12(2–3):231–254. https://doi.org/10.1016/0165-1889(88)90041-3
Kangalli USG, Uyar U, Balkan E (2023) Fundamental predictors of price bubbles in precious metals: a machine learning analysis. Mineral Econ 1–23. https://doi.org/10.1007/s13563-023-00404-z
Levendis JD (2018) Time series econometrics. Springer. https://doi.org/10.1007/978-3-319-98282-3
Liew VK (2004) Which lag length selection criteria should we employ? Econ Bull 3(33):1–9
Lüutkepohl H, Saikkonen P, Trenkler C (2001) Maximum eigenvalue versus trace tests for the cointegrating rank of a var process. Economet J 4(2):287–310. https://doi.org/10.1111/1368-423X.00068
Norgate T, Haque N (2010) Energy and greenhouse gas impacts of mining and mineral processing operations. J Clean Prod 18(3):266–274. https://doi.org/10.1016/j.jclepro.2009.09.020
Pearl J (2010) Causal inference, Causality: Objectives and Assessment. Proceedings of Machine Learning Research 6:39–58
Plourde A, Watkins GC (1998) Crude oil prices between 1985 and 1994: how volatile in relation to other commodities? Resour Energy Econ 20(3):245–262. https://doi.org/10.1016/S0928-7655(97)00027-4
Schwarz G (1978) Estimating the dimension of a model. The Ann Stat 6(2):461–464. https://doi.org/10.1214/aos/1176344136
Shahani R, Singhal U (2023) Do efficient commodity markets co-move: Evidence from Indian base metals market. Miner Econ 36(3):413–425. https://doi.org/10.1007/s13563-022-00353-z
Soytas U, Sari R, Hammoudeh S, Hacihasanoglu E (2009) World oil prices, precious metal prices and macroeconomy in Turkey. Energy Policy 37(12):5557–5566. https://doi.org/10.1016/j.enpol.2009.08.020
Zhang Y-J, Wei Y-M (2010) The crude oil market and the gold market: Evidence for cointegration, causality and price discovery. Resour Policy 35(3):168–177. https://doi.org/10.1016/j.resourpol.2010.05.003
Acknowledgements
This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC RGPIN-2019-04763) and the JSC Center of the International Program ‘Bolashak’ of the Republic of Kazakhstan. The authors are grateful for this support.
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Zhanbolat Magzumov: Literature review, data processing, methodology development, conducting case studies, and writing and revising the manuscript.
Mustafa Kumral: Conceptualization, supervision, resources, review and editing, funding acquisition, revising the manuscript, and project administration.
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Magzumov, Z., Kumral, M. Cointegration and causality testing in time series for multivariate analysis through minerals industry case studies. Miner Econ (2024). https://doi.org/10.1007/s13563-024-00435-0
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DOI: https://doi.org/10.1007/s13563-024-00435-0