I've heard that equations of motion with third- or higher-order time derivatives have problems with causality, but can't seem to find any proof or reasoning for this. Could anyone please help me? I need an answer as precise as possible for my thesis (if possible, it would be helpful if you could answer me in the framework of relativistic quantum mechanics).
Edit: my definition of causality would be the most generic possible, that is, the principle by which effects always follow from their causes and not vice versa. To be more specific at the cost of maybe limiting too much the scope of possible answers, I'm working with propagators and in that context causality takes the form of boundary conditions such as $G(x,t;x',t')=0$ for $t<t'$.