Bitcoin price prediction is a substantial challenge for cryptocurrency investors. This study offers an innovative scheme to predict Bitcoin returns and volatilities using a hybrid model that incorporates the autoregressive fractionally integrated moving average (ARFIMA), empirical wavelet (EW) transform, and local linear wavelet neural network (LLWNN) approaches to produce an ARFIMA-EWLLWNN model. Our methodologies integrate the advantages of the long-memory model, EW decomposition technique, artificial neural network structure, and backpropagation and particle swarm optimization learning algorithms. The experimental results of the optimized hybrid approach outperform some classic models by providing more accurate out-of-sample forecasts over longer horizons. The model proves to be the most appropriate Bitcoin forecasting technique. Moreover, the implemented method produces smaller prediction errors than other computing techniques.