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Gated Recurrent Neural Networks (RNNs) such as LSTM and GRU have been highly effective in handling sequential time series data in recent years. Although Gated RNNs have an inherent ability to learn complex temporal dynamics, there is potential for further enhancement by enabling these deep learning networks to directly use time information to recognise time-dependent patterns in data and identify important segments of time. Synonymous with time series data in real-world applications are missing values, which often reduce a model’s ability to perform predictive tasks. Historically, missing values have been handled by simple or complex imputation techniques as well as machine learning models, which manage the missing values in the prediction layers. However, these methods do not attempt to identify the significance of data segments and therefore are susceptible to poor imputation values or model degradation from high missing value rates. This paper develops Cyclic Gate enhanced recurrent neural networks with learnt waveform parameters to automatically identify important data segments within a time series and neglect unimportant segments. By using the proposed networks, the negative impact of missing data on model performance is mitigated through the addition of customised cyclic opening and closing gate operations. Cyclic Gate Recurrent Neural Networks are tested on several sequential time series datasets for classification performance. For long sequence datasets with high rates of missing values, Cyclic Gate enhanced RNN models achieve higher performance metrics than standard gated recurrent neural network models, conventional non-neural network machine learning algorithms and current state of the art RNN cell variants.