Locally Stationary Time Series and Multiscale Methods for Statistics (LuSTruM)

局部平稳时间序列和多尺度统计方法 (LuSTruM)

• 批准号: EP/K020951/1
• 负责人: Guy Nason
• 金额: $ 114.92万
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FK020951%2F1
• 关键词: Locally; Stationary; Time; Series; Multiscale

This fellowship proposes research in time series analysis and regression. Time seriesanalysis is concerned with data recorded through time. Time series occur in a varietyof areas of great importance to society such as medicine (recording of vital signs),economics and finance (GDP or share prices), the environment (air pollution),energy (national electricity demand), and transportation (traffic flow), to name but a few.A common way of displaying time series, often seen in the media, is via the time plot,which plots the series' values consecutively through time enabling major features,such as trend or seasonal effects, to be readily observed. Collectively, society needsto ensure that series are properly collected and recorded, modelled appropriately,to gain an understanding of their behaviour, and often predicted to estimate theirfuture values (forecasting).Much real world analysis assumes that series arise from stationary models, whichpermit the values of the series to change at each time, but the underlying statisticsdo not change (for example, a stationary share price changes from hour to hour,but the overall level, or mean, stays constant). It is becoming increasingly clear thatstationary models are not appropriate for many real series. For example, share pricestatistics do change, sometimes exceptionally, due to sudden events such as politicalupheaval or natural disasters, and often nonstationary models are appropriate anduseful alternatives.This project intends to develop nonstationary techniques with a focus on energy andeconomics applications. For example, energy companies are interested in nonstationarymodels because deregulation and increasingly diverse energy sources have causedmany previously stable data sets to become less stationary and more unpredictable.This project will create new nonstationary models intended to be more realistic, flexible andlead to better modelling, forecasting and consequently better decision-making.Nonstationary models can also shed light on tasks that are infeasible for stationary onessuch as ascertaining whether a series has been sampled frequently enough. We will alsoresearch nonstationary functional models, where each observation is not a single numberbut an entire curve, such as national electricity consumption recorded across a day.Regression is concerned with the modelling of relationships between different variablesand is used extensively in the real world. Many important regression methods assumethat data have constant variance and a `bell-curve' distribution. Much real data are notlike that, but operations, such as taking each observation's square root, can make thedata fulfil those constant variance/`bell curve' assumptions, at least approximately.Recently, a new, promising, very different, multiscale class, called the Haar-Fisz transform,was developed. The new class works extremely well for count data and has shown somefascinating theoretical properties, such as mimicking the well-known logarithm. This projectwill investigate the intriguing theoretical underpinnings of this new class as well as developfurther methods for cleaning up noisy signals, for example, removing noise from astronomicalor low-light security images. Additionally, we will investigate regression for irregular datausing techniques that make use of multiple scales simultaneously (multiscale).First generation multiscale methods, highly valued for purposes such as image compressionin JPEG, are not easily adapted to irregular situations. This project seeks to investigatesecond generation multiscale methods, suitable for irregular data. For example, to betterestimate and control information on networks (such as identify and mitigate delays ontransport networks) or irregularly-spaced systems (such as identify regions of the genomethat are implicated in several complex diseases such as cancer.)

该奖学金旨在研究时间序列分析和回归。时间序列分析关注的是通过时间记录的数据。时间序列发生在对社会非常重要的各个领域，例如医学（生命体征记录）、经济和金融（GDP或股价）、环境（空气污染）、能源（全国电力需求），交通（交通流），仅举几个例子，在媒体中经常看到的显示时间序列的常见方式是经由时间图，该系统将数列的数值随时间连续地绘制出来，使主要特征，例如趋势或季节性影响，易于观察。总的来说，社会需要确保正确收集和记录系列，适当建模，以了解其行为，并经常预测以估计其未来价值许多真实的世界分析都假设序列是从平稳模型中产生的，平稳模型允许序列的值在每一时刻发生变化，但基本的平稳性不变（例如，固定的股价每小时都在变化，但总体水平或均值保持不变）。人们越来越清楚地认识到，静态模型不适合于许多真实的序列。例如，股票价格统计数据确实会发生变化，有时会由于政治动荡或自然灾害等突发事件而发生异常变化，而非平稳模型通常是合适和有用的替代方案。本项目旨在开发非平稳技术，重点是能源和经济学应用。例如，能源公司对非平稳模型很感兴趣，因为放松管制和日益多样化的能源导致许多以前稳定的数据集变得不那么平稳和更加不可预测。该项目将创建新的非平稳模型，旨在更真实，更灵活，并导致更好的建模，更好的预测，更好的决策，非平稳模型还可以揭示一些平稳模型不可行的任务，例如确定一个系列是否被足够频繁地采样。我们还将研究非平稳函数模型，其中每个观测值不是一个单一的数字，而是一条完整的曲线，例如一天内记录的全国用电量。回归涉及不同变量之间关系的建模，并广泛用于真实的世界。许多重要的回归方法假定数据具有恒定方差和“钟形曲线”分布。许多真实的数据并非如此，但运算，如对每个观测值取平方根，可以使数据至少近似地满足这些恒定方差/“钟形曲线”假设。最近，一种新的、有前途的、非常不同的多尺度类被开发出来，称为Haar-Fisz变换。这个新的类对于计数数据工作得非常好，并且显示了一些迷人的理论属性，例如模仿众所周知的对数。该项目将研究这一新类别的有趣的理论基础，并进一步开发清理噪声信号的方法，例如，从天文或低光安全图像中去除噪声。此外，我们将研究不规则数据的回归，使用同时使用多尺度的技术（多尺度）。第一代多尺度方法，对于JPEG中的图像压缩等目的非常重要，不容易适应不规则的情况。该项目旨在研究第二代多尺度方法，适用于不规则数据。例如，为了更好地评估和控制网络上的信息（如识别和减轻传输网络上的延迟）或不规则间隔的系统（如识别与癌症等几种复杂疾病有关的基因组区域）。

项目成果

The local partial autocorrelation function and some applications

• DOI: 10.1214/20-ejs1748
• 发表时间: 2020-01
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Rebecca Killick;M. Knight;G. Nason;I. Eckley

Spectral correction for locally stationary Shannon wavelet processes

局部平稳香农小波过程的谱校正

• DOI: 10.1214/14-ejs880
• 发表时间: 2014
• 期刊: Electronic Journal of Statistics
• 影响因子: 1.1
• 作者: Eckley I

A new method for computing the projection median, its influence curve and techniques for the production of projected quantile plots.

计算投影中位数的新方法、其影响曲线以及生成投影分位数图的技术。

• DOI: 10.1371/journal.pone.0229845
• 发表时间: 2020
• 期刊: PloS one
• 影响因子: 3.7
• 作者: Chen F

Costationarity of Locally Stationary Time Series Using costat

使用 costat 的局部平稳时间序列的共平稳性

• DOI: 10.18637/jss.v055.i01
• 发表时间: 2013
• 期刊: Journal of Statistical Software
• 影响因子: 5.8
• 作者: Cardinali A

T-tubule disease: Relationship between t-tubule organization and regional contractile performance in human dilated cardiomyopathy.

• DOI: 10.1016/j.yjmcc.2015.04.022
• 发表时间: 2015-07
• 期刊: JOURNAL OF MOLECULAR AND CELLULAR CARDIOLOGY
• 影响因子: 5
• 作者: Crossman, David J.;Young, Alistair A.;Ruygrok, Peter N.;Nason, Guy P.;Baddelely, David;Soeller, Christian;Cannell, Mark B.
• 通讯作者: Cannell, Mark B.