We present a novel methodology for modeling and forecasting multivariate realized volatilities using customized graph neural networks to incorporate spillover effects across stocks. The proposed model offers the benefits of incorporating spillover effects from multi-hop neighbors, capturing nonlinear relationships, and flexible training with different loss functions. Our empirical findings provide compelling evidence that incorporating spillover effects from multi-hop neighbors alone does not yield a clear advantage in terms of predictive accuracy. However, modeling nonlinear spillover effects enhances the forecasting accuracy of realized volatilities, particularly for short-term horizons of up to one week. Moreover, our results consistently indicate that training with the Quasi-likelihood loss leads to substantial improvements in model performance compared to the commonly-used mean squared error. A comprehensive series of empirical evaluations in alternative settings confirm the robustness of our results.

Recently, end-to-end trained models for multiple-choice commonsense question answering (QA) have delivered promising results. However, such question-answering systems cannot be directly applied in real-world scenarios where answer candidates are not provided. Hence, a new benchmark challenge set for open-ended commonsense reasoning (OpenCSR) has been recently released, which contains natural science questions without any predefined choices. On the OpenCSR challenge set, many questions require implicit multi-hop reasoning and have a large decision space, reflecting the difficult nature of this task. Existing work on OpenCSR sorely focuses on improving the retrieval process, which extracts relevant factual sentences from a textual knowledge base, leaving the important and non-trivial reasoning task outside the scope. In this work, we extend the scope to include a reasoner that constructs a question-dependent open knowledge graph based on retrieved supporting facts and employs a sequential subgraph reasoning process to predict the answer. The subgraph can be seen as a concise and compact graphical explanation of the prediction. Experiments on two OpenCSR datasets show that the proposed model achieves great performance on benchmark OpenCSR datasets.

Although the state-of-the-art traditional representation learning (TRL) models show competitive performance on knowledge graph completion, there is no parameter sharing between the embeddings of entities, and the connections between entities are weak. Therefore, neighbor aggregation-based representation learning (NARL) models are proposed, which encode the information in the neighbors of an entity into its embeddings. However, existing NARL models either only utilize one-hop neighbors, ignoring the information in multi-hop neighbors, or utilize multi-hop neighbors by hierarchical neighbor aggregation, destroying the completeness of multi-hop neighbors. In this paper, we propose a NARL model named RMNA, which obtains and filters horn rules through a rule mining algorithm, and uses selected horn rules to transform valuable multi-hop neighbors into one-hop neighbors, therefore, the information in valuable multi-hop neighbors can be completely utilized by aggregating these one-hop neighbors. In experiments, we compare RMNA with the state-of-the-art TRL models and NARL models. The results show that RMNA has a competitive performance.