Temporal complex event forecasting aims to predict the future events given the observed events from history. Most formulations of temporal complex event are unstructured or without extensive temporal information, resulting in inferior representations and limited forecasting capabilities. To bridge these gaps, we innovatively introduce the formulation of Structured, Complex, and Time-complete temporal event (SCTc-TE). Following this comprehensive formulation, we develop a fully automated pipeline and construct a large-scale dataset named MidEast-TE from about 0.6 million news articles. This dataset focuses on the cooperation and conflict events among countries mainly in the MidEast region from 2015 to 2022. Not limited to the dataset construction, more importantly, we advance the forecasting methods by discriminating the crucial roles of various contextual information, i.e., local and global contexts. Thereby, we propose a novel method LoGo that is able to take advantage of both Local and Global contexts for SCTc-TE forecasting. We evaluate our proposed approach on both our proposed MidEast-TE dataset and the original GDELT-TE dataset. Experimental results demonstrate the effectiveness of our forecasting model LoGo. The code and datasets are released via https://github.com/yecchen/GDELT-ComplexEvent.