DF检验式中联合检验F统计量分布特征

单位根检验同被检验的模型中是否存在常数项、时间趋势项密切相关，针对常数项和时间趋势项及其t统计量的分布特征目前得到了很好的研究，但是相应的联合检验F统计量研究很少，而Hatanka（1996）就提到了该统计量的重要性，并认为有必要对其分布特征进行研究。本文通过蒙特卡罗模拟，分析了DF检验式中联合检验F统计量的分布特征，在此基础上给出了有限样本条件下各检验统计量的响应面函数，从而使得单位根检验进一步完善。     

退势单位根检验小样本性质的比较

在经验研究中，尽管Dickey—Fuller检验的DF统计量是应用最广泛的单位根检验，但是，它的检验功效偏低是众所周知的。为了改善Dickey—Fuller检验的功效，本文将时间序列的退势和DF检验、wS检验、MAX检验和RMA检验相结合，通过蒙特卡洛模拟试验研究了20种单位根检验的小样本性质，研究发现，对时间序列的退势(demeaning／detrencling)均能不同程度地改善单位根检验的功效；时间序列的递归退势RMA检验(RMA—ROLS检验)具有最理想的小样本性质，它的检验功效高于其他检验，其次是基于G15退势的DF检验(DF—G15检验)。     

单位根"伪检验"解析--以GDP时间序列为例

本文基于单位根检验的方法、步骤，结合我国GDP时间序列数据，分析单位根“伪检验”（spurious test）的五种类型，提出了相应改进意见。     

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。     

中国证券市场效率检验的模型设计

本文通过应用单位根检验、时间序列自相关检验、协整检验、因果检验等分析工具，提出中国证券市场效率检验模型的整体设计构想。     

中国股票市场有效性实证检验

本文以上证综指和深证成指的变化行为为研究对象，用单位根、方程比（VR）和序列二阶相关性检验方法（BDS）对其是否服从随机游走过程进行检验，从而判断中国股票市场弱式有效性是否成立。结果发现：虽然两指数行为服从单位根过程，且上证综指和深证成指序列在同方差情形上基本能够满足序列一阶不相关，但异方差情形下却是序列一阶相关，而BDS检验说明差异方差情形普遍存在。结论：中国股票市场弱式有效性并不成立。     

同期相关面板数据退势单位根检验的小样本性质

本文基于SUR回归将时间序列的两种单位根检验（ADF—GLS检验）推广到面板数据，得到了同期相关面板数据退势单位根检验，称为SUR—ADF—GLS检验。通过蒙特卡洛试验研究发现，SUR—ADF—GLS检验具有良好的小样本性质。并且，SUR—ADF—GLS检验关于面板数据的同期相关性结构存在着较强的“依存性”。     

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。     

面板数据单位根检验的一个简明蒙特卡洛实验框架

本文考虑到构成面板数据之横截面时间序列扰动项之间的关联性和异质性，设计出一个简明的蒙特卡洛实验框架以生成面板数据单位根检验统计值之有限样本密度分布和对应临界值。我们设计的蒙特卡洛框架提供了一个简明的可操作平台，可以运用于涉及到面板数据单位根检验的相关实证研究。     

依次检验策略中检验功效的Monte Carlo模拟及策略改进

依次检验策略是实施单位根检验的重要途径,但该策略并没有考虑低检验功效的影响。本文通过Monte Carlo实验,模拟了依次检验策略中的检验功效,发现在样本容量较小的情况下,该检验具有很低的检验功效。另外,本文从理论上分析了产生低功效的原因,并对该策略提出了改进。最后,采用改进后的检验策略,通过对上证综合指数序列的单位根检验验证了改进后策略的有效性。     

Unit root tests in panel data: asymptotic and finite-sample properties

We consider pooling cross-section time series data for testing the unit root hypothesis. The degree of persistence in individual regression error, the intercept and trend coefficient are allowed to vary freely across individuals. As both the cross-section and time series dimensions of the panel grow large, the pooled t-statistic has a limiting normal distribution that depends on the regression specification but is free from nuisance parameters. Monte Carlo simulations indicate that the asymptotic results provide a good approximation to the test statistics in panels of moderate size, and that the power of the panel-based unit root test is dramatically higher, compared to performing a separate unit root test for each individual time series.     

Trend‐stationary GNP: evidence from a new exact pointwise most powerful invariant unit root test

There has been a substantial debate whether GNP has a unit root. However, statistical tests have had little success in distinguishing between unit‐root and trend‐reverting specifications because of poor statistical properties. This paper develops a new exact small‐sample, pointwise most powerful unit root test that is invariant to the unknown mean and scale of the time series tested, that generates exact small‐sample critical values, powers and p‐values, that has power which approximates the maximum possible power, and that is highly robust to conditional heteroscedasticity. This test decisively rejects the unit root null hypothesis when applied to annual US real GNP and US real per capita GNP series. This paper also develops a modified version of the test to address whether a time series contains a permanent, unit root process in addition to a temporary, stationary process. It shows that if these GNP series contain a unit root process in addition to the stationary process, then it is most likely very small. Copyright © 2001 John Wiley & Sons, Ltd.     

Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics

Trend breaks appear to be prevalent in macroeconomic time series, and unit root tests therefore need to make allowance for these if they are to avoid the serious effects that unmodelled trend breaks have on power. Carrion-i-Silvestre et al. (2009) propose a pre-test-based approach which delivers near asymptotically efficient unit root inference both when breaks do not occur and where multiple breaks occur, provided the break magnitudes are fixed. Unfortunately, however, the fixed magnitude trend break asymptotic theory does not predict well the finite sample power functions of these tests, and power can be very low for the magnitudes of trend breaks typically observed in practice. In response to this problem we propose a unit root test that allows for multiple breaks in trend, obtained by taking the infimum of the sequence (across all candidate break points in a trimmed range) of local GLS detrended augmented Dickey–Fuller-type statistics. We show that this procedure has power that is robust to the magnitude of any trend breaks, thereby retaining good finite sample power in the presence of plausibly-sized breaks. We also demonstrate that, unlike the OLS detrended infimum tests of Zivot and Andrews (1992), these tests display no tendency to spuriously reject in the limit when fixed magnitude trend breaks occur under the unit root null.     

Unemployment hysteresis in Australia: evidence using nonlinear and stationarity tests with breaks

This study is an attempt to test the hysteresis versus the natural rate hypothesis in unemployment rate using time series data of the Australia covering the period 1978: 2–2010:12. For the analysis, we employed nonlinear as well as different linear tests (with incorporation of endogenously determined structural breaks) of unit root. We found that the Australian unemployment rate is nonlinear process, has a partial unit root and trend reverting. Therefore, we provide support for the structuralist hypothesis. This finding provides the importance of accounting for exogenous shocks in the series and gives support to the shifting natural-rate hypothesis of the Australian unemployment rate.     

Testing for Unit Roots with Breaks: Evidence on the Great Crash and the Unit Root Hypothesis Reconsidered

Nelson and Plosser (1982), in a classic paper, failed to find strong evidence against the null hypothesis of a generating process with a unit autoregressive root for thirteen US macroeconomic time series. Perron (1989) claimed that such evidence was available for a majority of these series if the alternative hypothesis was of trend stationarity with a break in 1929. Zivot and Andrews (1992) treated the break date as endogenous, then finding strong evidence agcainst the null for a minority of these series. Our own analysis extends theirs by permitting a break under the null as well as the alternative hypothesis, and allowing for the sequential nature of the testing. Our empirical findings complete the circle. We find no strong evidence against the unit root hypothesis for any of the thirteen Nelson–Plosser series.     

Tests for Multiple Breaks in the Trend with Stationary or Integrated Shocks

In this paper, we propose new tests of the presence of multiple breaks in the trend of a univariate time‐series where the number and dates of the breaks are unknown and that are valid in the presence of stationary or unit root shocks. These tests can also be used to sequentially estimate the number of breaks. The behaviour of the proposed tests is studied through Monte Carlo experiments.     

Tests for Stationarity in Series with Endogenously Determined Structural Change*

We consider tests of the null hypothesis of stationarity against a unit root alternative, when the series is subject to structural change at an unknown point in time. Three extant tests are reviewed which allow for an endogenously determined instantaneous structural break, and a related fourth procedure is introduced. We further propose tests which permit the structural change to be gradual rather than instantaneous, allowing the null hypothesis to be stationarity about a smooth transition in linear trend. The size and power properties of the tests are investigated, and the tests are applied to four economic time series.     

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。     

Trends in international commodity prices: Panel unit root analysis

The purpose of this paper is to examine the behavior of international commodity prices within the context of the Prebisch–Singer hypothesis. To this end, I utilize a panel unit root approach which is able to account for multiple structural breaks and cross-section dependency. The unit root analysis for 24 international commodity prices during the period 1900–2003 shows evidence in favor of the trend stationary process in the commodity prices. The results thereby imply that shocks to commodity prices are temporary in nature and tend to be corrected over time. The estimation of the trend stationary models indicates that the Prebisch–Singer hypothesis is not a universal phenomenon.     

To criticize the critics: An objective bayesian analysis of stochastic trends

In two recent articles, Sims (1988) and Sims and Uhlig (1988/1991) question the value of much of the ongoing literature on unit roots and stochastic trends. They characterize the seeds of this literature as ‘sterile ideas’, the application of nonstationary limit theory as ‘wrongheaded and unenlightening’, and the use of classical methods of inference as ‘unreasonable’ and ‘logically unsound’. They advocate in place of classical methods an explicit Bayesian approach to inference that utilizes a flat prior on the autoregressive coefficient. DeJong and Whiteman adopt a related Bayesian approach in a group of papers (1989a,b,c) that seek to re-evaluate the empirical evidence from historical economic time series. Their results appear to be conclusive in turning around the earlier, influential conclusions of Nelson and Plosser (1982) that most aggregate economic time series have stochastic trends. So far these criticisms of unit root econometrics have gone unanswered; the assertions about the impropriety of classical methods and the superiority of flat prior Bayesian methods have been unchallenged; and the empirical re-evaluation of evidence in support of stochastic trends has been left without comment. This paper breaks that silence and offers a new perspective. We challenge the methods, the assertions, and the conclusions of these articles on the Bayesian analysis of unit roots. Our approach is also Bayesian but we employ what are known in the statistical literature as objective ignorance priors in our analysis. These are developed in the paper to accommodate explicitly time series models in which no stationarity assumption is made. Ignorance priors are intended to represent a state of ignorance about the value of a parameter and in many models are very different from flat priors. We demonstrate that in time series models flat priors do not represent ignorance but are actually informative (sic) precisely because they neglect generically available information about how autoregressive coefficients influence observed time series characteristics. Contrary to their apparent intent, flat priors unwittingly bias inferences towards stationary and i.i.d. alternatives where they do represent ignorance, as in the linear regression model. This bias helps to explain the outcome of the simulation experiments in Sims and Uhlig and some of the empirical results of DeJong and Whiteman. Under both flat priors and ignorance priors this paper derives posterior distributions for the parameters in autoregressive models with a deterministic trend and an arbitrary number of lags. Marginal posterior distributions are obtained by using the Laplace approximation for multivariate integrals along the lines suggested by the author (Phillips, 1983) in some earlier work. The bias towards stationary models that arises from the use of flat priors is shown in our simulations to be substantial; and we conclude that it is unacceptably large in models with a fitted deterministic trend, for which the expected posterior probability of a stochastic trend is found to be negligible even though the true data generating mechanism has a unit root. Under ignorance priors, Bayesian inference is shown to accord more closely with the results of classical methods. An interesting outcome of our simulations and our empirical work is the bimodal Bayesian posterior, which demonstrates that Bayesian confidence sets can be disjoint, just like classical confidence intervals that are based on asymptotic theory. The paper concludes with an empirical application of our Bayesian methodology to the Nelson-Plosser series. Seven of the 14 series show evidence of stochastic trends under ignorance priors, whereas under flat priors on the coefficients all but three of the series appear trend stationary. The latter result corresponds closely with the conclusion reached by DeJong and Whiteman (1989b) (based on truncated flat priors). We argue that the DeJong-Whiteman inferences are biased towards trend stationarity through the use of flat priors on the autoregressive coefficients, and that their inferences for some of the series (especially stock prices) are fragile (i.e. not robust) not only to the prior but also to the lag length chosen in the time series specification.