New challenges in time series analysis

时间序列是对一个或多个数量的观察，通过时间收集。它们出现在人类活动的许多重要领域，例如金融（富时100指数的每日收盘价；一种金融工具随时间变化的订单簿）、经济学（央行设定的利率；宏观经济指标的月度变化；收益率曲线随时间变化）、工程学（语音信号）、自然科学（温度、地震信号）和神经科学（通过脑电图、功能磁共振成像或其他技术测量大脑活动），等等。时间序列分析师面临的典型任务包括了解时间序列的性质和建模，预测其未来值，了解它如何影响和受其他因素的影响，并将其分类为若干类别之一。妥善解决这些问题，可以对经济和社会产生巨大的积极影响。现代时间序列数据集经常违背传统的统计假设。在许多情况下，时间序列数据具有巨大的规模和高维性（例如在宏观经济建模中，许多潜在的预测因素经常包含在模型中，例如GDP增长），非正态分布（例如在金融中，许多金融工具的日回报显示偏离正态）和非平稳，这意味着它们的统计属性，如平均值，方差或自协方差随时间变化（例如，在金融领域，市场的相互依赖结构在金融危机时期已知会发生变化）。通常，时间序列数据以复杂对象的形式出现，如曲线（如收益率曲线）。需要新的理论和方法来处理这些新的情况。所提出的研究将在非平稳、高维和曲线值时间序列的分析方面开辟新的领域。虽然我们提出解决的许多问题是由金融应用驱动的，但我们的解决方案将可转移到其他领域。特别是，我们将(i)重新定义人们思考非平稳性的方式。我们将把（非）平稳性定义为与问题相关的，而不是时间序列的“固定”属性，并根据这一新观点提出新的统计模型选择程序。这将导致（非）平稳性的概念在解决实际问题（如预测）时得到比目前更好的应用；（ii）为高维和非平稳的时间序列提出新的、问题相关的降维方法（降维在实践中很有用，因为低维时间序列更容易处理）。我们希望这种问题依赖的方法将引发一种全新的思考高维时间序列数据和一般高维数据的方式；（iii）提出了高维时间序列回归问题（包括非平稳设置）统计模型选择的新方法。我们的新方法将在金融预测或统计市场研究等领域发挥作用；（iv）研究高维时间序列（如金融回报）中统计模型选择的新方法，其中依赖结构因“冲击”（如宏观经济公告）而突然变化；(v)提出新的多尺度时间序列模型，专门用于解决金融领域长期存在的问题，即在多个时间尺度（例如日内和日间）上对金融回报进行一致建模；（vi）提出分析时间序列曲线（如收益率曲线）的新方法，这些曲线可以以各种方式是非平稳的。总的来说，这是一个全面而雄心勃勃的研究计划，旨在为现代时间序列分析中一些最重要的问题提供新颖的解决方案。

Time series are observations on a quantity or quantities, collected through time.They arise in many important areas of human endeavour, for examplefinance (daily closing values of the FTSE 100 index; the order book of a financialinstrument evolving over time), economics (interest rates set by a central bank;monthly changes to macroeconomic indicators; yield curves changing through time), engineering (speech signals), natural sciences (temperature, seismic signals) and neuroscience (brain activity measurements via EEG, fMRI or other techniques), to name but a few. Typical tasks faced by time series analysts include understanding the nature of and modelling the evolution of the time series, forecasting its future values, understanding how it impacts and is impacted by other factors, and classifying it to one of a number of categories. Solving these tasks adequatelycan have enormous positive impact on economy and society.Modern time series datasets often defy traditional statistical assumptions. In many contexts, time series data are massive in size and high-dimensional (e.g. in macroeconomic modelling, where many potential predictors are frequently included in models e.g. for GDP growth), non-normally-distributed (e.g. in finance where daily returns on many financial instruments show deviations from normality) and non-stationary, which means that their statistical properties such as the mean, variance or autocovariance change through time (e.g. in finance where co-dependence structure of markets is known to change in times of financial crises). Often, time series data arise as complex objects such as curves (e.g. yield curves). New theories and methods are needed to handle these new settings.The proposed research will break new ground in the analysis of non-stationary,high-dimensional and curve-valued time series. Although many of the problems we propose to tackle are motivated by financial applications, our solutions will be transferable to other fields. In particular, we will(i) re-define the way in which people think of non-stationarity. We will define (non-)stationarity to be a problem-dependent, rather than `fixed' property of time series, and propose new statistical model selection procedures in accordance with this new point of view. This will lead to the concept of (non-)stationarity beingput to much better use in solving practical problems (such as forecasting) thanit so far has been;(ii) propose new, problem-dependent dimensionality reduction procedures for time series which are both high-dimensional and non-stationary (dimensionality reductionis useful in practice as low-dimensional time series are much easier to handle). We hope that this problem-dependent approach will induce a completely new way of thinking of high-dimensional time series data and high-dimensional data in general;(iii) propose new methods for statistical model selection in high-dimensional time series regression problems, including the non-stationary setting. Our new methods will be useful in fields such as financial forecasting or statistical market research;(iv) investigate new methods for statistical model selection in high-dimensional time series (of, e.g., financial returns) in which the dependence structure changes in an abrupt fashion due to `shocks', e.g. macroeconomic announcements;(v) propose new multiscale time series models, specifically designed to solve a long-standing problem in finance of consistent modelling of financial returns on multiple time scales, e.g. intraday and interday;(vi) propose new ways of analysing time series of curves (e.g. yield curves) which can be non-stationary in a variety of ways.Overall, this is a comprehensive and ambitious research programme, which aims tooffer novel solutions to some of the most important questions in modern time seriesanalysis.