A discrete-time non-linear time series system of a cascade structure is identified. The system consists of a non-linear memoryless element followed by a dynamic linear subsystem. The non-linear characteristic is recovered with the help of the kernel regression estimate. The consistency of the estimate in the presence of correlated noise is examined. The rate of convergence as well as some variance reduction method are established. Data-driven techniques for selection of a smoothing parameter are discussed. The identification of a linear part of the system is also studied