带有结构突变的单位根检验 ——文献综述

单位根检验是时间序列分析的基础，而是否考虑结构突变对单位根检验的结论有着重要影响，因此，考虑结构突变的单位根检验已成为计量经济学界的一个前沿热点问题。本文回顾了这一问题的发展历史，总结了该领域已取得的一些重要研究成果，最后对该问题最新的发展动向加以概括。     

考虑结构突变的单位根检验程序研究——基于“新息异常值模型”的Perron检验分析

Perron检验是一种考虑结构突变的单位根检验方法,检验统计量的分布依赖于数据生成过程中所包含的确定性趋势和所选取的检验回归式;而在实证分析中真实的数据生成过程是未知的,这使得单位根检验缺乏必要依据,因而探寻科学有效的单位根检验程序是受到广泛关注的问题。基于此,本文在"IO模型"分析框架下,依据Perron检验提出了一套考虑结构突变的单位根检验程序,并通过蒙特卡洛模拟分析了该程序在有限样本情形下的表现。本研究完善了带有结构突变的单位根检验理论,为实证分析提供了有益的建议和参考。     

结构突变时间序列单位根的"伪检验"

利用蒙特卡罗分析方法,本文对含一个结构变化点的经济变量单位根检验的有效性进行了探讨。分析的结果表明,当经济变量的数据生成过程存在一个结构性突变时,不考虑这种变化而进行常规的单位根检验只有在特定条件下才不会“失效”:只有当突变前后两期的样本数相差极大,或者选取的样本期总数很小时,单位根检验才不会“失效”。并且,随着结构变化程度的增大,不考虑结构变化而进行常规单位根检验得出“伪检验”的可能性也会增大。     

购买力平价与金融危机基于结构突变下的面板单位根检验

本文采用外生结构突变下面板数据单位根检验方法和传统的检验方法，比较研究了东南亚七国或地区的实际汇率受金融危机冲击的影响，发现东南亚七国或地区的实际汇率是带有结构突变的退势平稳过程，外生结构突变条件下的面板单位根检验结果支持购买力平价理论，实际汇率对购买力平价的背离是短期的：但在不考虑结构突变的情况下，却得出不同的结论，而蒙特卡洛模拟实验表明前者更为可信。     

关于机理变化型变结构非线性协整的研究

变结构非线性协整是协整理论发展的必然的趋势,也是经济系统复杂多变的必然需求,文章补充了变结构非线性协整的定义,并提出了机理变化型变结构非线性协整,指出其本质问题即单位根的结构突变检验,总结了几种结构突变的单位根检验方法,讨论了变结构点的估计方法,给出了基于Chow统计量的变结构协整检验和建模方法。     

人民币汇率购买力平价问题的重新研究——基于结构突变检验与变结构协整的视角

本文应用LM结构突变检验以及Gregory-Hansen等变结构协整方法,对人民币汇率购买力平价问题进行了重新研究。研究发现样本期内人民币汇率发生了两次结构突变,第一次发生在2005年7月,第二次发生在2006年12月。LM检验显示,发生了结构突变的汇率数据生成过程仍为单位根过程,意味着某些经济冲击确实对数据生成过程(DGP)产生了实质影响。进一步对比研究发现,在未考虑结构突变情况下,样本期内购买力平价不成立;但在考虑结构突变情况下,两种变结构协整方法都支持购买力平价成立。     

考虑结构突变时确定性趋势的估计与单位根检验式的选择——基于可行广义最小二乘估计的分析

单位根的检验功效依赖于回归检验式中的确定性趋势,而趋势估计量的分布又取决于序列的平稳性,两者相互制约。鉴于此,本文借鉴了Perron和Yabu(2009)提出的可行广义最小二乘估计,推导了相关统计量的分布,在考虑结构突变的情况下,构造了一套确定性趋势的估计和推断程序,并通过蒙特卡罗模拟对该程序的有限样本性质进行了分析。结论显示,大多数情形下根据该程序进行的单位根检验具有较高功效。     

多种单位根检验法的比较研究

本文基于单位根检验基本原理,比较了5种单位根检验的方法,说明在小样本情况下,为提高检验功效,应针对数据生成过程的特点联合多种检验法进行检验。如果检验变量为非平稳,则需要进行进一步的结构突变检验,本文主张选用结构突变点内生的Perron检验法与外生检验法相结合来判断变量的平稳性。     

一种结构突变面板数据单位根的联合检验

本文根据Banerjee等(1992)的模型变换方法和内生突变点选择原理,得到了一种纵剖面时间序列相互独立面板数据的内生结构突变单位根的联合检验——■_T~*(λ)检验。并且,基于泛函中心极限定理推导出了该检验统计量的渐近分布;通过蒙特卡洛模拟实验讨论了该检验的实际检验水平以及面板数据的样本大小、异质性、截距突变的幅度、斜率突变的幅度和结构突变位置等因素对检验功效的影响。最后,根据1952～2006年中国27个省份的数据讨论了人均实际收入的稳定性。     

带结构突变的确定趋势的单位根检验方法——兼对中国工农业产品比价的实证分析

存在未知结构突变点的DGP关于结构突变的信息是不完全的,理论上不可能得到媲美标准ADF检验或Perron检验的统计特性,且Perron检验比标准ADF检验更适合于作为其单位根统计量的极限分布。本文以Perron(2009)方法为基础,结合minSSR和FGLS详细讨论结构突变的单位根检验的三个步骤,澄清了很多模糊的认识。以我国工农业产品比价和工农业产品价格指数为例,本文的实证研究发现,中国工农业利益分配格局的重大改变是由国际经济事件造成的冲击引起的。     

International evidence on persistence in output in the presence of an episodic change

This paper uses some newly developed methods and techniques to examine the dynamic properties of international output in the presence of a structural break. We provide statistical evidence to show that the unit root test results can, in some cases, be sensitive to whether a one-time structural break in the data is modelled exogenously or endogenously. However, in most cases the unit root test results remain robust to specification of the structural break exogenously or endogenously; moreover, we find that the null hypothesis of a unit root in output can be rejected in favour of a ‘flexible’ trend alternative for a number of countries such as Canada, Denmark, France, and the United States.     

A Unit Root Test Using a Fourier Series to Approximate Smooth Breaks*

We develop a unit‐root test based on a simple variant of Gallant's (1981) flexible Fourier form. The test relies on the fact that a series with several smooth structural breaks can often be approximated using the low frequency components of a Fourier expansion. Hence, it is possible to test for a unit root without having to model the precise form of the break. Our unit‐root test employing Fourier approximation has good size and power for the types of breaks often used in economic analysis. The appropriate use of the test is illustrated using several interest rate spreads.     

Is There a Natural Rate of Crime?

Studies in the economics of crime literature have reached mixed conclusions on the deterrence hypothesis. One explanation that has been offered for the failure to find evidence of a deterrent effect in the long run is the natural rate of crime. This article applies univariate unit root tests to crime series for the United Kingdom and United States and panel unit roots to crime rates for a panel of G7 countries to examine whether there is a natural rate of crime. Our main finding is that when we allow for two structural breaks in the univariate unit root test and a structural break in the panel data unit root test, there is strong evidence of a natural rate of crime. The policy implications of our findings is that governments should focus on altering the economic and social structural profile that determines crime in the long run rather than increasing expenditure on law enforcement that will at best reduce crime rates in the short run.     

Detection of Structural Change in the Long‐run Persistence in a Univariate Time Series*

In this paper, we investigate a test for structural change in the long‐run persistence in a univariate time series. Our model has a unit root with no structural change under the null hypothesis, while under the alternative it changes from a unit‐root process to a stationary one or vice versa. We propose a Lagrange multiplier‐type test, a test with the quasi‐differencing method, and ‘demeaned versions’ of these tests. We find that the demeaned versions of these tests have better finite‐sample properties, although they are not necessarily superior in asymptotics to the other tests.     

Are unemployment rates in OECD countries stationary? Evidence from univariate and panel unit root tests

This paper revisits the dynamics of unemployment rate for 29 OECD countries over the period of 1980–2013. Numerous empirical studies of the dynamics of unemployment rate are carried out within a linear framework. However, unemployment rate can show nonlinear behaviour as a result of business cycles or some idiosyncratic factors specific to labour market (Cancelo, 2007). Thus, as a testing strategy, we first perform Harvey, Leybourne, and Xiao (2008) linearity unit root test and then apply the newly ESTAR nonlinear unit root test suggested by Kruse (2011). This test has higher power than conventional unit root tests when time series exhibits nonlinear behaviour. Our empirical findings provide significant evidence in favour of unemployment rate stationarity for 25 countries. For robustness purpose, we have also used panel unit root tests without and with structural breaks. The empirical results show that unemployment hysteresis hypothesis is strongly rejected, when taking into account the cross-sectional and structural break assumptions. Thus, unemployment rate is expected to return back to their natural levels without executing any costly macroeconomic labour market policies by the OECD’s governments.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice-versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.     

Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1

This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice‐versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.