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Abstract Like how useful weather forecasting is, the capability of forecasting or predicting cyber threats can never be overestimated. Previous investigations show that cyber attack data exhibits interesting phenomena, such as long-range dependence and high nonlinearity, which impose a particular challenge on modeling and predicting cyber attack rates. Deviating from the statistical approach that is utilized in the literature, in this paper we develop a deep learning framework by utilizing the bi-directional recurrent neural networks with long short-term memory, dubbed BRNN-LSTM. Empirical study shows that BRNN-LSTM achieves a significantly higher prediction accuracy when compared with the statistical approach.

Causality is an intriguing concept that once tamed, can have many applications. While having been widely investigated in other domains, its relevance and usefulness in the cybersecurity domain has received little attention. In this paper, we present a systematic investigation of a particular approach to causality, known as Granger causality (G-causality), in cybersecurity. We propose a framework, dubbed Cybersecurity Granger Causality (CGC), for characterizing the presence of G-causality in cyber attack rate time series and for leveraging G-causality to predict (i.e., forecast) cyber attack rates. The framework offers a range of research questions, which can be adopted or adapted to study G-causality in other kinds of cybersecurity time series data. In order to demonstrate the usefulness of CGC, we present a case study by applying it to a particular cyber attack dataset collected at a honeypot. From this case study, we draw a number of insights into the usefulness and limitations of G-causality in the cybersecurity domain.