Detecting causal relations among symbolic time series

Symbolic time series analyses are used in economics and other social sciences as a way of reducing the impact of noise on data and to exhibit more clearly the evolution of time series. We show that causality tests applied to symbolic series may fail to detect actual relations or generate statistical artifacts. Well-known causality detection methods, like transfer entropy, Granger's test, or Peter-Clark Momentary Conditional Independence (PCMCI), may miss some existing causal relationships or, more frequently, yield non-existent ones. The performance of these methods may differ, depending on the specific choices of lag structures and alphabet sizes, as well as on the characteristics of the underlying dynamic process.