Cointegration and causality testing in time series for multivariate analysis through minerals industry case studies

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.