Formalizing multiresolution statistical causality tests: A comprehensive review and empirical analysis

In recent years, there has been significant progress in utilizing multiresolution analysis (MRA) to analyze multi-dimensional financial time series, providing a nuanced approach to decision-making processes. MRA models, employing a multiscale econometric strategy, are particularly effective for intricate commodity time series, such as power prices, characterized by a multilevel structure and extreme volatility. Traditional causality tests, like Granger tests, often fall short in offering comprehensive insights in these scenarios. As a response, MRA-based scale-by-scale causality tests have emerged as potent and user-friendly tools for examining predictability in non stationary time series, enhancing decision-making capabilities. Despite their significance, a gap exists in the literature concerning the mechanisms, implementations, and methodologies underlying these tests. This article aims to formalize multiresolutional causality tests, delineate different approaches, and discuss their properties within the context of decision-making. The simulation experiments highlight the strengths and limitations of these tests, particularly during periods of heightened volatility in power markets, providing crucial insights for more informed decision-making. Moreover, an empirical analysis conducted during the COVID-19 pandemic, incorporating price data and vaccination rates, underscores the practical applicability of these statistical tests in understanding market dynamics amid a global crisis. The results reveal the significant impact of the pandemic on volatility and price transmission, illustrating the utility of multiresolution analysis in capturing the evolving interdependencies. The article concludes with a robustness check on simulated data, further affirming the reliability and robustness of the proposed methodology.