After publishing four articles utilizing a new method for the statistical study of climate time series, we found it useful to provide a detailed review of the method itself, which is the primary objective of this work. Unlike the methods most commonly used by scientists analyzing such data, this new method does not seek to identify trends for explorative forecasts. Instead, it enables the detection of precise signals indicating interactions with other climate entities, thereby enhancing our understanding of the underlying phenomena. As illustrated through three example articles, the mechanisms uncovered using this method can be integrated into a mathematical model. The simulations thus obtained are more deterministic than stochastic – a significant advantage for producing high-quality forecasts in the context of global warming. Even if this was the sole application of the method, it would be sufficient to demonstrate its value. However, as a final example detailed in this work shows, reconsidering the original series using different periods (e.g., month, quarter, semester, year) can further refine our understanding of the mechanisms at play. We conclude this work by exploring the potential applicability of this method for analyzing non-climatic temporal data series.