发帖
雷达卡
摘要翻译：
为了更好地理解大型经济金融时间序列的空间结构，并为构造半参数模型提供指导，本文首先考虑用硬阈值正则化方法估计广义$M$相关和$Beta$-混合时间序列（含有$J$变量和$T$观测值）的大空间协方差矩阵，只要${{\log J\，\cx^*(\ct)}/{T}=\co(1)$（前者带有一定的时间相关性测度$\cx^*(\ct)$)或$\log J/{T}=\co(1)$（后者带有一定的上界混合系数）。我们量化了估计量的一致性率和时间依赖水平之间的相互作用，讨论了一种直观的阈值选择重采样方案，并证明了一个通用的交叉验证结果。给出一个一致估计的协方差（相关）矩阵，利用其与图形模型和半参数的自然联系，在“筛选”解释变量后，实现了一种新的前向（后向）标号置换过程来聚类“相关”变量，构造相应的半参数模型，并进一步用带符号约束的分组降维方法估计该模型。我们称之为SCE（Screen-Cluster-Estimation）方法，用于复杂空间结构的高维数据建模。最后，将该方法应用于经济金融时间序列的空间结构研究，找到了适合于居民消费价格指数(CPI)估计的半参数结构，说明了该方法优于线性模型。
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英文标题：
《Dynamic Large Spatial Covariance Matrix Estimation in Application to
Semiparametric Model Construction via Variable Clustering: the SCE approach》
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作者：
Song Song
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最新提交年份：
2011
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分类信息：
一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
To better understand the spatial structure of large panels of economic and financial time series and provide a guideline for constructing semiparametric models, this paper first considers estimating a large spatial covariance matrix of the generalized $m$-dependent and $\beta$-mixing time series (with $J$ variables and $T$ observations) by hard thresholding regularization as long as ${{\log J \, \cx^*(\ct)}}/{T} = \Co(1)$ (the former scheme with some time dependence measure $\cx^*(\ct)$) or $\log J /{T} = \Co(1)$ (the latter scheme with some upper bounded mixing coefficient). We quantify the interplay between the estimators' consistency rate and the time dependence level, discuss an intuitive resampling scheme for threshold selection, and also prove a general cross-validation result justifying this. Given a consistently estimated covariance (correlation) matrix, by utilizing its natural links with graphical models and semiparametrics, after "screening" the (explanatory) variables, we implement a novel forward (and backward) label permutation procedure to cluster the "relevant" variables and construct the corresponding semiparametric model, which is further estimated by the groupwise dimension reduction method with sign constraints. We call this the SCE (screen - cluster - estimate) approach for modeling high dimensional data with complex spatial structure. Finally we apply this method to study the spatial structure of large panels of economic and financial time series and find the proper semiparametric structure for estimating the consumer price index (CPI) to illustrate its superiority over the linear models.
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PDF链接：
https://arxiv.org/pdf/1106.3921
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