Comparing Quantization Methods for Testing Causality between Continuous-state Discrete-time Processes

This paper investigates the use of the plug-in directed information rate estimator and hypothesis testing to detect causality between discrete-time continuous-state processes. Following our previous work, we have first quantized the continuous-state processes by means of three quantization methods: equidistant, equipopulated and symbolic. Then, we have applied directed information rate estimation and hypothesis testing. Simulations indicate that the symbolic method is the most effective in discriminating cases with an underlying causality from those with abscent causality.