Bayesian Learning of Relational Graph in Semiparametric High-dimensional Time Series
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AI 根据所提供的论文材料归类：摘要研究高维时间序列，并明确使用美国 GDP 分行业数据预测未来观测。
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半参数高维时间序列关系图的贝叶斯学习
- 研究问题
- 如何在高维时间序列中同时刻画时间依赖和分量之间的图关系，并以可计算的贝叶斯方法估计结构、预测未来观测？
- 方法与思路
- 作者将独立单变量潜在序列正交旋转并作稀疏线性变换，对谱密度、旋转矩阵和共同精度矩阵设先验，以 Whittle 近似开展推断。
- 材料陈述的贡献
- 摘要称提出 OUT 模型、后验计算算法和伪后验收敛理论，并在一定时间依赖条件下获得类似独立观测的收缩率。
- 阅读关注点
- 应核对图结构与变换的对应关系、模型识别、Whittle 近似条件，以及谱平滑度要求、后验计算收敛和预测评估设计。
- 阅读边界
- 这是 arXiv 预印本，同行评审及期刊接收未核实；摘要未给出具体收缩率和完整条件，也未提供美国 GDP 应用的预测误差。
原文摘要
Time series data arising in many applications nowadays are high-dimensional. A large number of parameters describe features of these time series. We propose a novel approach to modeling a high-dimensional time series through several independent univariate time series, which are then orthogonally rotated and sparsely linearly transformed. With this approach, any specified intrinsic relations among component time series given by a graphical structure can be maintained at all time snapshots. We call the resulting process an Orthogonally-rotated Univariate Time series (OUT). Key structural properties of time series such as stationarity and causality can be easily accommodated in the OUT model. For Bayesian inference, we put suitable prior distributions on the spectral densities of the independent latent times series, the orthogonal rotation matrix, and the common precision matrix of the component times series at every time point. A likelihood is constructed using the Whittle approximation for univariate latent time series. An efficient Markov Chain Monte Carlo (MCMC) algorithm is developed for posterior computation. We study the convergence of the pseudo-posterior distribution based on the Whittle likelihood for the model's parameters upon developing a new general posterior convergence theorem for pseudo-posteriors. We find that the posterior contraction rate for independent observations essentially prevails in the OUT model under very mild conditions on the temporal dependence described in terms of the smoothness of the corresponding spectral densities. Through a simulation study, we compare the accuracy of estimating the parameters and identifying the graphical structure with other approaches. We apply the proposed methodology to analyze a dataset on different industrial components of the US gross domestic product between 2010 and 2019 and predict future observations.