ACCEPTED MANUSCRIPT A Vine Copula Model for Predicting the Effectiveness of Cyber Defense Early-Warning

Internet-based computer information systems play critical roles in many aspects of the modern society. However, these systems are constantly under cyber attacks that can cause catastrophic consequences. In order to defend these systems effectively, it is necessary to measure and predict the effectiveness of cyber defense mechanisms. In this paper, we investigate how to measure and predict the effectiveness of an important cyber defense mechanism that is known as early-warning. This turns out to be a challenging problem because we must accommodate the dependence among certain 4-dimensional time series. In the course of using a dataset to demonstrate the prediction methodology, we discover a new non-exchangeable and rotationally symmetric dependence structure, which may be of independent value. We propose a new vine copula model to accommodate the newly discovered dependence structure, and show that the new model can predict the effectiveness of early-warning more accurately than the others. We also discuss how to use the prediction methodology in practice.