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、方差和自协方差会随着时间的推移而变化，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或金融理论经常预测的那样，包含任何序列之间的长期关系的信息。协整分析提供了一种解决方案，它承认变量的某些组合是平稳的（稳定的）。一个关键的例子是期限结构数据，在这些数据中经常发现，虽然个别利率似乎不稳定，但利率之间的息差似乎稳定。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/政策的变化）而变得复杂。经验证据表明，这些事件往往表现为变量的潜在确定性趋势成分的多重变化和/或未预料到的随机冲击的波动性变化。当这些形式的结构变化存在时，现存的协整检验可能导致关于变量之间存在或不存在长期关系的误导性推断。这通常会导致错误的计量经济模型和较差的预测能力。因此，开发新的协整测试非常重要，它可以在这种环境中提供可靠的推断。这样做构成了这个项目的第一部分，并将涉及一个新的基于模拟（引导）程序的开发。鉴于最近的金融危机，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（如汇率、股票价格）和宏观经济（如国内生产总值）数据频率之间不匹配的计量经济学方法，这构成了该项目的第二部分。虽然金融数据可以非常频繁地观察到，但宏观经济数据通常最多只能每月获得一次。绝大多数建模多变量时间序列的方法都假设一个共同的采样频率；这通常需要通过将高频数据转换为最低频率来丢弃信息。然而，高频金融数据包含可能影响低频数据未来时间路径的信息，其利用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，可以在观察到金融危机对GDP的影响之前很长时间观察到金融危机，但使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的能力可能对政策制定有重要帮助。在处理混合频率数据时，还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检验了非恒定波动率的行为，这种检验不允许趋势中的结构性变化。钱伯斯最近开发了结合混合频率数据的方法，保留了序列之间的潜在关系，并分析了时间聚合下的协整系统。这个项目将建立在这些基础之上。理论结果的实际相关性将通过模拟实验来探讨。我们还将通过关键国际数据集上的工作实例，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.