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As the demand for renewable energy is increasing, wind speed forecasting (WSF) becomes increasingly popular and essential for wind power generation. Several methods have been developed in the literature for WSF. However, WSF accuracy is challenging to obtain due to its non-stationary and non-linear character. To overcome this issue, this study suggests a novel integrated forecasting model for WSF. In the majority of cases, decomposition techniques are essential for removing noise and extracting patterns from non-stationary and non-linear wind speed time series. Among these decomposition techniques, the most widely used decomposition methods based on frequency domain theory are the Fourier decomposition method (FDM), the empirical wavelet transform (EWT), and the variational mode decomposition (VMD). However, FDM decomposition gives inconsistent results, EWT has mixed problems, and VMD is unsuitable for non-stationary time series. Thus, a novel combined model based on empirical Fourier decomposition (EFD) techniques, long short-term memory (LSTM) neural networks, and the Grey Wolf optimizer (GWO) is proposed in this paper. Initially, the wind speed time series is decomposed using EFD into a set of sub-series and a residual, which is a stationary sub-series that can be easily modelled by a recurrent neural network (RNN). Further, the matching LSTM is used to forecast each sub-series and residual, while the GWO optimizes the sub-series estimated output, resulting in improved prediction precision and stability. In order to assess the model performance, five wind speed datasets from various places in India are employed. The findings show that the proposed model is the top performing model among the other ten models; The average statistical score obtained from all datasets reduces 11.01% in the mean absolute error (MAE), 10.68% in the root mean square error (RMSE) and 10.73% in the mean absolute percentage error (MAPE). Further, regularity conditions for universal consistency of proposed model is also proved mathematically. • A novel hybrid EFD-LSTM-GWO architecture for wind speed forecasting. • Resolving the mixed-mode, inconsistent, and non-stationary challenges. • Analysing the proposed model's universal consistency. • Outperformance of the proposed algorithm over other existing models. [ABSTRACT FROM AUTHOR]