We propose a nonparametric and time-varying directed information graph
(TV-DIG) framework to estimate the evolving causal structure in time series
networks, thereby addressing the limitations of traditional econometric models
in capturing high-dimensional, nonlinear, and time-varying interconnections
among series. This framework employs an information-theoretic measure rooted in
a generalized version of Granger-causality, which is applicable to both linear
and nonlinear dynamics. Our framework offers advancements in measuring systemic
risk and establishes meaningful connections with established econometric
models, including vector autoregression and switching models. We evaluate the
efficacy of our proposed model through simulation experiments and empirical
analysis, reporting promising results in recovering simulated time-varying
networks with nonlinear and multivariate structures. We apply this framework to
identify and monitor the evolution of interconnectedness and systemic risk
among major assets and industrial sectors within the financial network. We
focus on cryptocurrencies' potential systemic risks to financial stability,
including spillover effects on other sectors during crises like the COVID-19
pandemic and the Federal Reserve's 2020 emergency response. Our findings
reveals significant, previously underrecognized pre-2020 influences of
cryptocurrencies on certain financial sectors, highlighting their potential
systemic risks and offering a systematic approach in tracking evolving
cross-sector interactions within financial networks.

我们提出了一个非参数的、时变的有向信息图（TV-DIG）框架来估计时间序列网络中不断演变的因果结构，从而解决传统计量经济模型在捕捉高维度、非线性和时变的系列之间相互关联方面的局限性。通过仿真实验和经验分析，我们评估了所提出模型的有效性，并报告了在恢复具有非线性和多变量结构的模拟时变网络方面取得的有希望的结果。我们将该框架应用于识别和监测金融网络中主要资产和行业部门之间的相互关系和系统风险的演变。我们着重研究加密货币对金融稳定性的潜在系统性风险，包括在 COVID-19 大流行和 2020 年美联储紧急响应期间对其他部门的溢出效应。我们的研究发现，在 2020 年之前，加密货币对某些金融部门产生了重要且以前未被认可的影响，突显了它们的潜在系统风险，并在跟踪金融网络内不断演化的跨部门互动方面提供了一种系统方法。

建模系统风险：一种时变非参数因果推理框架

Modeling Systemic Risk: A Time-Varying Nonparametric Causal Inference  Framework

Time-varying stochastic optimization problems frequently arise in machine
learning practice (e.g. gradual domain shift, object tracking, strategic
classification). Although most problems are solved in discrete time, the
underlying process is often continuous in nature. We exploit this underlying
continuity by developing predictor-corrector algorithms for time-varying
stochastic optimizations. We provide error bounds for the iterates, both in
presence of pure and noisy access to the queries from the relevant derivatives
of the loss function. Furthermore, we show (theoretically and empirically in
several examples) that our method outperforms non-predictor corrector methods
that do not exploit the underlying continuous process.

本文针对机器学习中涉及到的时间变化的随机优化问题，以及其在离散时间的解法中存在的连续性问题，提出了基于预测 - 校正算法的优化方法，并给出了理论与实验证明，相较于不使用该算法的其他方法，本文提出的算法能更好地利用连续过程，提高最优解的准确性和鲁棒性。