The remaining useful life (RUL) prediction of wind turbine planetary gearboxes is crucial for the reliable operation of new energy power systems. However, the interpretability of the current RUL prediction models is not satisfactory. To this end, a multi-stage RUL prediction model is proposed in this work, with an interpretable metric-based feature selection algorithm. In the proposed model, the advantages of neural networks and long-range-dependent stochastic processes are combined. In the offline training stage, a general representation of the degradation trend is learned with the meta-long short-term memory neural network (meta-LSTM) model. The inevitable measurement error in the sensor reading is modelled by white Gaussian noise. During the online RUL prediction stage, fractional generalized Pareto motion (fGPm) with an adaptive diffusion is employed to model the stochasticity of the planetary gearbox degradation. In the case study, real planetary gearbox degradation data are used for the model validation.