Abstract Hypergraphs generalize graphs by allowing each edge, known as a hyperedge, to connect multiple vertices. Despite their significant advantages, hypergraph embeddings have been underexplored compared to pairwise graphs due to the inherent complexity of the hypergraph topologies. Existing approaches often rely on fixed-dimensional embeddings, where the relative closeness among nodes is fixed, regardless of hyperedge order. This fixed-dimensional setting encourages heredity among hyperedges of different orders and fails to offer a flexible projection to capture the complex relationships among nodes. In this project, we propose a novel increasing dimensional embedding approach that jointly considers sparsity and node heterogeneity, including both degree heterogeneity and node heterogeneity in the latent dependencies among hyperedges of different orders. The proposed framework offers a more flexible approach to capturing diverse features of hypergraphs and could potentially provide new insights in different real applications.

Abstract To investigate the fundamental relationship between business cycle synchronisation (BCS) and trade/finance intensities, we develop the simultaneous equation panel data model that accommodates all the key elements: simultaneity, spatial spillovers, global shocks and parameter heterogeneity. We propose the consistent CCEX-2SLS estimator and conduct a spatial network analysis to investigate the direct and indirect impacts of trade/finance intensities on the BCS across country-pairs or the selected clusters. We apply the proposed approach to the dataset consisting of the 136 pairs of the 17 OECD countries over 1995Q1-2019Q4, and convincingly unveil: (i) the individual CCEX-2SLS estimation results demonstrate the importance of explicitly taking parameter heterogeneity into account; (i) almost 90% of the samples belong to cases where the direct and indirect effects of trade/finance intensities on BCS display opposite signs; (iii) we observe the surprisingly negative total effect of trade intensity on BSC and negative spillovers of trade and financial intensities on BCS. This implies that the optimal currency area (OCA) criteria have not yet fulfilled in the EU and suggests that policymakers coordinate across borders and mitigate adverse economic fluctuations to facilitate trade/financial intensities for improved BCS.

Abstract Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures synchronized 5-minute volume intervals across multiple assets. While traditional matrix time series focus mainly on temporal evolution, our approach incorporates both spatial and temporal dynamics, enabling simultaneous analysis of interactions across multiple dimensions. The inherent endogeneity in spatio-temporal autoregressive models renders ordinary least squares estimation inconsistent. To overcome this difficulty while simultaneously estimating two distinct weight matrices with banded structure, we develop an iterated generalized Yule-Walker estimator by adapting a generalized method of moments framework based on Yule-Walker equations. Moreover, unlike conventional models that employ a single bandwidth parameter, the dual-bandwidth specification in our framework requires a new two-step, ratio-based sequential estimation procedure.