Structural Changes, Level Shifts in Variance and the Frequency of Permanent Shocks

该项目的共同主题是经济时间序列的结构性变化，但开发的一些工具将用于该主题之外。有五个主要的项目描述，每个项目都可以导致几篇研究论文发表在领先的期刊上。1）测试在线性回归模型中的误差方差的多个结构变化，允许或同时测试条件均值回归的参数变化。该项目提供的方法的基础上的一个可能性框架的一些测试问题和估计的方差和系数的中断的数量，并评估是否有些是共同的。2）股票收益率（代理的绝对收益率）的变异性的时间序列属性。本计画考虑一个简单的随机电平漂移模型，并提出一种基于混合正态分布状态空间模型的估计方法。它展示了如何扩展该模型，使转变的概率成为其他变量的函数，从而提供更好的预测。该项目建立了一个随机模型，可以提供在任何给定时期的水平移动或斜率变化的概率估计。通常的单位根模型指定概率为1，而对于趋势平稳过程，概率为0。 这种方法可以提供一个相当广泛的图片，这可以提供有用的实际含义。4）评估的重要性，在非趋势性的经济和金融时间序列通过其自相关函数的形状。5）另一种方法来评估的性质的结构变化测试。该项目使用Bahadur效率的概念来比较结构变化测试的性质，并表明与常用的局部渐近功率分析相比，它产生的预测与有限样本性能更好地吻合。它提出了推导测试，巴哈杜尔最优的一个广泛的足够class.Broader影响：在这个项目中提出的工作将是有价值的应用研究人员在各个领域，以及计量经济学家和统计学家。它不仅提供了新的工具来回答感兴趣的经济（和其他）问题，而且还包含了大量的经验成分，可以为如何建模经济变量提供新的思路，特别是在宏观经济学和金融领域。

The common theme of this project is structural change in economic time series but some tools developed will be used beyond this topic. There are five main projects described, each of which can lead to several research papers to be published in leading journals.1) Testing for multiple structural changes in the variance of the errors in a linear regression model allowing for or testing concurrently for changes in the parameters of the conditional mean regression. This project provides methods based on a likelihood framework for a number of testing problems and for estimating the number of breaks in variance and in coefficients and to assess whether some are common.2) The time series properties of the variability of stock returns (proxied by absolute returns). This project considers a simple stochastic level shift model and propose a method of estimation based on a State Space model with a mixture of Normal distribution. It shows how the model can be extended to allow the probability of shifts to be a function of other variables and, hence, deliver improved forecasts.3) The frequency of permanent shocks. The project builds a stochastic model which can deliver estimates of the probability of a level shift or a slope change at any given period. The usual unit root model specifies the probability to be one, while for a trend-stationary process it is zero. This method allows a considerably broader picture, which can deliver useful practical implications.4) Assessing the importance of level shifts in non-trending economic and financial time series via the shape of their autocorrelation function.5) An alternative approach to evaluate the properties of structural change tests. This project uses the concept of Bahadur efficiency to compare the properties of tests for structural changes and show that it yields predictions in better agreement with the finite sample performance compared to the often used local asymptotic power analysis. It proposes deriving tests that are Bahadur optimal within a broad enough class.Broader Impact: The work proposed in this project will be valuable to applied researchers in various fields as well as to econometricians and statisticians. It not only provides new tools to answer economic (and other) questions of interest but also contains substantial empirical components that can shed new light on how to model economic variables, especially in the areas of macroeconomics and finance.