Understanding the properties exhibited by large scale network probing traffic would improve cyber threat intelligence. In addition, the prediction of probing rates is a key feature for security practitioners in their endeavors for making better operational decisions and for enhancing their defense strategy skills. In this work, we study different aspects of the traffic captured by a /20 network telescope. First, we perform an exploratory data analysis of the collected probing activities. The investigation includes probing rates at the port level, services interesting top network probers and the distribution of probing rates by geolocation. Second, we extract the network probers exploration patterns. We model these behaviors using transition graphs decorated with probabilities of switching from a port to another. Finally, we assess the capacity of Non-stationary Autoregressive and Vector Autoregressive models in predicting port probing rates as a first step towards using more robust models for better forecasting performance.