To study the dynamical mechanism which generates Parkinsonian resting tremor, we apply coupling directionality analysis to local field potentials (LFP) and accelerometer signals recorded in an ensemble of 48 tremor epochs in four Parkinsonian patients with depth electrodes implanted in the ventro-intermediate nucleus of the thalamus (VIM) or the subthalmic nucleus (STN). Apart from the traditional linear Granger causality method we use two nonlinear techniques: phase dynamics modelling and nonlinear Granger causality. We detect a bidirectional coupling between the subcortical (VIM or STN) oscillation and the tremor, in the theta range (around 5 Hz) as well as broadband (>2 Hz). In particular, we show that the theta band LFP oscillations definitely play an efferent role in tremor generation, while beta band LFP oscillations might additionally contribute. The brain-->tremor driving is a complex, nonlinear mechanism, which is reliably detected with the two nonlinear techniques only. In contrast, the tremor-->brain driving is detected with any of the techniques including the linear one, though the latter is less sensitive. The phase dynamics modelling (applied to theta band oscillations) consistently reveals a long delay in the order of 1-2 mean tremor periods for the brain-->tremor driving and a small delay, compatible with the neural transmission time, for the proprioceptive feedback. Granger causality estimation (applied to broadband signals) does not provide reliable estimates of the delay times, but is even more sensitive to detect the brain-->tremor influence than the phase dynamics modelling.