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In this paper, we introduce a deep spiking delayed feedback reservoir (DFR) model to combine DFR with spiking neuros: DFRs are a new type of recurrent neural networks (RNNs) that are able to capture the temporal correlations in time series while spiking neurons are energy-efficient and biologically plausible neurons models. The introduced deep spiking DFR model is energy-efficient and has the capability of analyzing time series signals. The corresponding field programmable gate arrays (FPGA)-based hardware implementation of such deep spiking DFR model is introduced and the underlying energy-efficiency and recourse utilization are evaluated. Various spike encoding schemes are explored and the optimal spike encoding scheme to analyze the time series has been identified. To be specific, we evaluate the performance of the introduced model using the spectrum occupancy time series data in MIMO-OFDM based cognitive radio (CR) in dynamic spectrum sharing (DSS) networks. In a MIMO-OFDM DSS system, available spectrum is very scarce and efficient utilization of spectrum is very essential. To improve the spectrum efficiency, the first step is to identify the frequency bands that are not utilized by the existing users so that a secondary user (SU) can use them for transmission. Due to the channel correlation as well as users' activities, there is a significant temporal correlation in the spectrum occupancy behavior of the frequency bands in different time slots. The introduced deep spiking DFR model is used to capture the temporal correlation of the spectrum occupancy time series and predict the idle/busy subcarriers in future time slots for potential spectrum access. Evaluation results suggest that our introduced model achieves higher area under curve (AUC) in the receiver operating characteristic (ROC) curve compared with the traditional energy detection-based strategies and the learning-based support vector machines (SVMs).