The Analysis of Non-stationary Time Series in Economics and Finance: Co-integration, Trend Breaks, and Mixed Frequency Data

宏观经济和金融时间序列通常是非平稳的（或不稳定的），因为它们的均值、方差和自协方差随时间变化，因此标准的多变量时间序列模型只能有效地应用于这些变量的变化。然而，这些模型并不像经济学或金融学理论所预测的那样，包含任何关于系列之间长期关系的信息。协整分析提供了一个解决方案，它认识到某些变量的组合是平稳的（稳定的）。一个重要的例子是期限结构数据，在这种数据中，人们经常发现，虽然个别利率看起来不稳定，但利率之间的利差看起来稳定。实际的协整分析由于经济体周期性地经历结构性变化（如股市崩盘或政府制度/政策变化）而变得复杂。经验证据表明，这些事件往往表现为变量的基本确定性趋势成分的多重变化和/或意外随机冲击波动性的变化。现存的协整检验可能会导致误导性的推断，关于存在或变量之间的长期关系，当这些形式的结构变化存在。这通常会导致错误指定的预测能力差的计量经济学模型。因此，重要的是要开发新的协整检验，可以提供可靠的推断，在这样的环境。本研究的第一部分是开发新的模拟（bootstrap）程序。在最近的金融危机中，人们越来越关注宏观经济与金融部门之间的相互作用。为了有效地做到这一点，需要能够处理金融部门数据（如汇率、股票价格）和宏观经济数据（如GDP）出现频率之间不匹配的计量经济学方法，这构成了项目的第二部分。虽然可以非常频繁地观察金融数据，但宏观经济数据通常最多只能每月提供一次。绝大多数的方法建模多变量时间序列假设一个共同的采样频率，这通常需要丢弃的信息，在高频数据转换到最低频率。然而，高频金融数据包含的信息可能会影响低频数据的未来时间路径，利用高频金融数据可以使政策制定者在宏观经济数据可用之前迅速采取行动。例如，在观察到金融危机对国内生产总值的影响之前，很久就可以观察到金融危机，但是，利用能够处理混合频率数据的计量经济学模型预测这些影响可能是什么的能力，可以对决策提供重要帮助。在处理混合频率数据时，也将考虑允许结构变化的方法。理论发展将使用大样本计量经济学理论进行，将利用申请人的专业知识和经验。泰勒已经在协整检验中研究了非恒定波动的行为，协整检验不考虑趋势的结构变化。钱伯斯最近开发的方法相结合的混合频率的数据，保持系列之间的基本关系，并分析了共同整合的系统下的时间聚集。本项目将建立在这些基础之上，并将通过模拟实验探索理论结果的实际相关性。我们还将通过关键国际数据集的工作实例为实证研究人员提供明确的指导，并免费提供计算机程序，以促进新技术的实施。

Macroeconomic and financial time series are typically non-stationary (or unstable), in that their means, variances and autocovariances evolve over time, such that standard multivariate time series models can only be validly applied to the changes in these variables. Such models, however, contain no information about any long run relationships between the series, as are often predicted by economic or finance theory. A solution is provided by co-integration analysis which recognises that certain combinations of the variables are stationary (stable). A key example is term structure data, where it is often found that while individual interest rates appear to be unstable, the spreads between the rates appear stable.Practical co-integration analysis is complicated by the fact that economies periodically undergo episodes of structural change, such as stock market crashes or changes in government regime/policy. Empirical evidence suggests that these episodes often manifest themselves in the form of multiple changes in the underlying deterministic trend component of the variables and/or changes in the volatility of the unanticipated random shocks. Extant co-integration tests can result in misleading inference regarding the presence or otherwise of long run relationships between the variables when these forms of structural change are present. This will typically result in misspecified econometric models with poor forecasting ability. It is therefore important to develop new co-integration tests which can deliver reliable inference in such environments. Doing so constitutes the first part of this project and will involve the development of a new simulation-based (bootstrap) procedure.In light of the recent financial crisis, attention has increasingly focused on understanding the interactions between the macroeconomy and the financial sector. To do so effectively, econometric methods are needed that are capable of handling the mismatch between the frequencies at which data on the financial sector (eg exchange rates, stock prices) and the macroeconomy (eg GDP) become available, and this constitutes the second part of the project. While financial data can be observed at very high frequencies, macroeconomic data are typically available only monthly at best. The vast majority of methods for modelling multivariate time series assume a common sampling frequency; this typically entails discarding information in the high frequency data by converting it to the lowest frequency. However, high frequency financial data contains information that can affect the future time path of the low frequency data, and its utilisation can enable policymakers to act promptly prior to the macroeconomic data becoming available. For example, a financial crisis can be observed long before its effects on GDP are observed, but the ability to predict what those effects might be, using an econometric model capable of dealing with mixed frequency data, can be an important aid to policy making. Methods to allow for structural changes when dealing with mixed frequency data will also be considered.The theoretical development, to be conducted using large sample econometric theory, will exploit the expertise and experience of the applicants. Taylor has already examined the behaviour of non-constant volatility on co-integration tests which do not allow for structural change in the trend. Chambers has recently developed methods of combining mixed frequency data that preserve the underlying relationships between the series and has also analysed co-integrated systems under temporal aggregation. This project will build on these foundations.The practical relevance of the theoretical results will be explored using simulation experiments. We will also provide clear guidance to empirical researchers, through worked examples on key international datasets, and make freely available computer programs, to facilitate the implementation of the new techniques.