What if we intervene?: Higher-order cross-lagged causal model with interventional approach under observational design

Experimental design allows us to more accurately determine the causal relationship between variables correlated over time as compared to observational design based on conditional probability. Observational design allows us to establish merely a dependency relationships that helps predict the objective variable. However, under certain observational design conditions, it is possible to determine the causal effects of the experimental design without carrying out an intervention. In this work, we present a causal model of higher-order crossed lags capable of inferring causal relationships with hypothetical interventions under an observational design. Additionally, a visualization form is offered that allows us to analyze multiple interventions simultaneously. The methodology is applied to three financial series: the Euro–United States Dollar exchange rate; the Dow Jones Industrial Index; and Gold futures. An analysis of causality concerning their volatilities and differences between the approaches is presented as well as a classic approach of conditioning. Researchers must be cautious in defining the research objective and design for other studies since the approaches lead to very different causal conclusions. The framework presented is expected to be useful in any discipline where one wants to learn  What would happen if we intervene? without actually making an intervention.