Cyber attacks endanger physical, economic, social, and political security. There have been extensive efforts in government, academia, and industry to anticipate, forecast, and mitigate such cyber attacks. A common approach is time-series forecasting of cyber attacks based on data from network telescopes, honeypots, and automated intrusion detection/prevention systems. This research has uncovered key insights such as systematicity in cyber attacks. Here, we propose an alternate perspective of this problem by performing forecasting of attacks that are analyst-detected and -verified occurrences of malware. We call these instances of malware cyber event data. Specifically, our dataset was analyst-detected incidents from a large operational Computer Security Service Provider (CSSP) for the U.S. Department of Defense, which rarely relies only on automated systems. Our data set consists of weekly counts of cyber events over approximately seven years. This curated dataset has characteristics that distinguish it from most datasets used in prior research on cyber attacks. Since all cyber events were validated by analysts, our dataset is unlikely to have false positives which are often endemic in other sources of data. Further, the higher-quality data could be used for a number of important tasks for CSSPs such as resource allocation, estimation of security resources, and the development of effective risk-management strategies. To quantify bursts, we used a Markov model of state transitions. We used a Bayesian State Space Model for forecasting and found that events one week ahead could be predicted with reasonable accuracy, except for the bursts (~10% of the weeks). To quantify bursts, we used a Markov model of state transitions. Our findings of systematicity in analyst-detected cyber attacks are consistent with previous work using cyber attack data from other sources. The advanced information provided by a forecast may help with threat awareness by providing a probable value and range for future cyber events one week ahead, similar to a weather forecast. Other potential applications for cyber event forecasting include proactive allocation of resources and capabilities for cyber defense (e.g., analyst staffing and sensor configuration) in CSSPs. Enhanced threat awareness may improve cybersecurity by helping to optimize human and technical capabilities for cyber defense.