权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Modelling Vast Time Series: Sparsity and Segmentation

大规模时间序列建模：稀疏性和分段

基本信息

批准号：
EP/L01226X/1
负责人：
Qiwei Yao
金额：
$ 50.06万
依托单位：
London School of Economics and Political Science
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2014
资助国家：
英国
起止时间：
2014 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FL01226X%2F1
关键词：
Modelling Vast Time Series Sparsity

项目摘要

In this modern information age the availability of large or vast time series data brings opportunities with challenges to time series analysts. The demand for modelling and forecasting high-dimensional time series arises from various practical problems such as panel study of economic, social and natural phenomena (such as weather), financial market analysis and communications engineering. We propose two new approaches for analyzing high-dimensional time series data when the dimension is as large as, or even greater than, the length of observed time series. The first approach is to fit the data with sparse vector auto-regressive models (VAR). For some applications when the components are ordered, we will further explore the sparsity due to a band structure. Note that we impose sparsity or banding directly on the coefficient matrices in VAR models. Hence, the relevant inference methods and the associated theory are different from those for the estimation of large covariance matrices. Our second approach is segmentation via transformation. We seek for a contemporaneous linear transformation such that the transformed time series is divided into several sub-vectors, and those sub-vectors are both contemporaneously and serially uncorrelated. Therefore, they can be modelled separately.The challenges of our proposal are two-fold: First we need to develop the statistical inference methods and the associated theory for identifying the sparse structure and for fitting sparse VAR models with large dimensions. Let p denote the dimension of the time series. We aim to reduce the number of model parameters from the order of the square of p to the order of p, and to develop the valid inference methods when log(p)= o(n). Secondly, we need to identify the linear transformation to identify the latent segmentation structure, i.e. the block-diagonal autocovariance structure when such a structure exists.High-dimensional data analysis (i.e. 'big data') is one of the most vibrant research areas in statistics in the last decade. Most work to date concentrates on linear regression with a large number of candidate regressors (i.e. the so-called 'large p small n' paradigm). Another stream of the research is on the inference of large covariance matrices. Though bearing a similar banner, the problems addressed in the proposal are different, as we deal with high-dimensional time series and we need to estimate large transformation or coefficient matrices that are not positive semi-definite. We aim for simple and effective inference methods so that they can be implemented with ordinary PCs for the data of dimensions in the order of thousands.

在现代信息时代，大量时间序列数据的出现给时间序列分析带来了机遇和挑战。对高维时间序列建模和预测的需求来自各种实际问题，如经济，社会和自然现象（如天气）的面板研究，金融市场分析和通信工程。我们提出了两种新的方法来分析高维时间序列数据时，尺寸是一样大，甚至大于，观察到的时间序列的长度。第一种方法是用稀疏向量自回归模型（VAR）拟合数据。对于某些应用程序，当组件是有序的，我们将进一步探讨稀疏性，由于一个带结构。请注意，我们直接对VAR模型中的系数矩阵施加稀疏性或条带。因此，相关的推断方法和相关的理论是不同于那些大的协方差矩阵的估计。我们的第二种方法是通过转换进行分割。我们寻求一个同期的线性变换，使变换后的时间序列被分成几个子向量，这些子向量都是同期和串行不相关。我们的建议的挑战是双重的：首先，我们需要开发的统计推断方法和相关的理论，用于识别稀疏结构和拟合稀疏VAR模型与大尺寸。设p表示时间序列的维数。我们的目标是将模型参数的数量从p的平方的数量级减少到p的数量级，并在log（p）= o（n）时开发有效的推断方法。其次，我们需要识别线性变换来识别潜在的分割结构，即块对角自协方差结构（当这种结构存在时）。高维数据分析（即“大数据”）是近十年来统计学中最具活力的研究领域之一。迄今为止，大多数工作集中在具有大量候选回归变量的线性回归（即所谓的“大p小n”范式）。研究的另一个流是关于大协方差矩阵的推断。虽然具有类似的旗帜，但提案中解决的问题是不同的，因为我们处理高维时间序列，我们需要估计非半正定的大型变换或系数矩阵。我们的目标是简单而有效的推理方法，使他们可以实现与普通PC的数据的尺寸在数千的顺序。