Spurious Rejections with Endogenous Break Unit Root Tests in the Presence of Outliers and Breaks

Unit root tests with structural break developed by Zivot and Andrews (1992 Zivot , E. , Andrews , D. W. K. ( 1992 ). Further evidence on the great crash, the oil price shock and the unit root hypothesis . Journal of Business and Economic Statistics 10 : 251 – 270 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Perron and Rodriguez (2003 Perron , P. , Rodriguez , G. ( 2003 ). GLS detrending, efficient unit root tests and structural change . Journal of Econometrics 115 : 1 – 27 .[Crossref], [Web of Science ®] , [Google Scholar]) in the presence of additive outliers and breaks are studied by simulation experiments. The results show that the Zivot–Andrews test appears to have size distortions due to the additive outliers whereas the Perron–Rodriguez test exhibits good properties of size and power. However, the two tests are biased when a second break is present but not taken into account. Furthermore, these endogenous break unit root tests tend to determine the break point incorrectly at one period behind the true break point, leading to spurious rejections of the unit root null hypothesis.     

On the asymptotic distribution of a simple unit root test for trending and breaking series

In this paper, we derive the asymptotic distribution of Popp's (2008) innovational outlier unit root test for trending series with a break. The results of Zivot and Andrews (1992) are applied to provide the limiting results of these new test statistics. We tabulate their asymptotic and finite sample critical values, and illustrate the use of the new statistics with an application to the unemployment rate series for 23 OECD countries.     

New innovational outlier unit root test with a break at an unknown time

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.     

M-estimation for Moderate Deviations From a Unit Root

Phillips and Magdalinos (2007 Phillips, P., Magdalinos, T. (2007). Limit theory for moderate deviations from a unit root. J. Econometrics 136:115–130.[Crossref], [Web of Science ®] , [Google Scholar]) introduced a larger neighborhoods of one (called moderate deviations) than the conventional local to unity roots in autoregression models. Least square estimates (LSE) of the serial correlation coefficient were studied and asymptotics were provided. In this article, we investigate the M-estimation of the serial correlation coefficient having moderate deviations from the unit root. For both the near stationary case and explosive case, the Bahadur representations and limits in distribution are given for the M-estimators of the serial correlation coefficient. The limit theory demonstrates that the convergence rates of the M-estimators are the same as that for LSE hence bridging the very different convergence rates of the stationary and unit root cases. The limit theory also facilitates the comparison of the relative asymptotic efficiency among different estimators within the family of M-estimators.     

Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

A number of recent papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, taken the lag length in the unit root test regression to be a deterministic function of the sample size, rather than data-determined, the latter being standard empirical practice. We investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent lag selection methods in augmented Dickey–Fuller type regressions and propose new lag selection criteria which allow for unconditional heteroskedasticity. Standard lag selection methods are shown to have a tendency to over-fit the lag order under heteroskedasticity, resulting in significant power losses in the (wild bootstrap implementation of the) augmented Dickey–Fuller tests under the alternative. The proposed new lag selection criteria are shown to avoid this problem yet deliver unit root tests with almost identical finite sample properties as the corresponding tests based on conventional lag selection when the shocks are homoskedastic.     

Lag Length Selection in DF-GLS Unit Root Tests

We reinvestigate the empirical problem of lag length selection in unit root tests when using the augmented Dickey–Fuller test based on GLS-detrending. We extend the Ng and Perron (1995 Ng , S. , Perron , P. ( 1995 ). Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag . Journal of American Statistical Association 90 : 268 – 281 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) work on this issue by applying the finite sample critical values calculated using the formulae proposed by Cheung and Lai (1995 Cheung , Y. W. , Lai , K. S. ( 1995 ). Lag order and critical values of a modified Dickey–Fuller test . Oxford Bulletin of Business and Economics 57 : 411 – 418 .[Crossref] , [Google Scholar]). Unlike Ng and Perron (2001 Ng , S. , Perron , P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica 69:1519–1554.[Crossref], [Web of Science ®] , [Google Scholar]) we find through simulation studies that the method of selecting lag length using the sequential t-test in the ADF regression of GLS-detrended series performs the best in most cases.     

门限自回归下的单位根检验可靠性研究

在非对称的门限自回归模型下,由于传统单位根检验式的误设,会导致单位根检验势下降。本文通过一系列的Monte-Carlo模拟表明：非对称性对ADF和PP检验的检验势会产生较大影响,而对其他四种常用的单位根检验势产生的影响较小,也就是说,在非对称的门限自回归下,非对称性对退势单位根检验势产生的影响较小。模拟中也发现：NP单位根检验对TAR模型和持久性都具有稳健性。     

Testing for Unit Root Against Stationarity Using the Likelihood Ratio Test

In a first-order autoregressive model with drift, we derive the likelihood ratio test for a unit root against the stationary alternative. We also derive the test in a state space model with trend. Finite sample and asymptotic critical values are obtained by Monte Carlo simulations. A simulation study investigates the power performance of the likelihood ratio test and we also examine how a bias correction of the test affects the results.     

基于奇异值分解去势的非线性趋势序列单位根检验研究

 如何克服ADF与PP单位根检验法对非线性趋势平稳序列的伪检验,提高单位根检验的功效,是非平稳时间序列分析的重要问题。本文基于奇异值分解的思路,构造出检验非平稳时间序列单位根的SVD-RMA检验法,此方法将时间序列的趋势项与干扰项分离,然后用递归均值调整法对干扰项进行检验。仿真实验表明,SVD-RMA法对线性与非线性趋势、甚至结构突变过程的检验功效都非常好;对非线性趋势平稳的检验而言,SVD-RMA检验得到正确结论的可能性要远远好于ADF与PP检验。     

Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression

This paper provides a means of accurately simulating explosive autoregressive processes and uses this method to analyze the distribution of the likelihood ratio test statistic for an explosive second-order autoregressive process of a unit root. While the standard Dickey–Fuller distribution is known to apply in this case, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies. This has previously constituted a bar on supporting asymptotic results by means of simulation, and analyzing the finite sample properties of tests in the explosive region.     

Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression

This paper provides a means of accurately simulating explosive autoregressive processes and uses this method to analyze the distribution of the likelihood ratio test statistic for an explosive second-order autoregressive process of a unit root. While the standard Dickey-Fuller distribution is known to apply in this case, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies. This has previously constituted a bar on supporting asymptotic results by means of simulation, and analyzing the finite sample properties of tests in the explosive region.     

LSTAR-GARCH模型的单位根检验

LSTAR模型的单位根检验往往易忽视其条件方差的时变性,实际上,对许多经济变量尤其是金融变量建立LSTAR模型后,经常发现其条件方差存在GARCH效应。针对LSTAR-GARCH模型的平稳性检验,本文构建了检验统计量tNG,之后在极大似然估计的基础上,推导出tNG的渐近分布,通过蒙特卡洛模拟方法得到该统计量的渐近临界值,并在此基础上研究了tNG检验的检验功效。在与刘雪燕和张晓峒(2009)提出的tNL检验、Ling等(2003)提出的tLG检验以及DF单位根检验进行比较后,发现tNG检验具备明显优势。     

正交多项式逼近下非线性趋势序列单位根检验

 传统单位根检验方法常常假设带有线性的确定性趋势,但如果趋势是非线性的,通常将因为检验功效大幅下降而导致检验失败。本文研究用正交多项式逼近非线性趋势,然后对残差进行单位根检验的方法。研究了用正交多项式进行趋势逼近的性质,推导了这种方法进行单位根检验时统计量的极限分布,提出了正交多项式最高阶数的确定方法,仿真研究了残差相关与不相关时的检验功效。结果表明,检验方法是有效的。     

“堤坝”型结构突变的时间序列单位根检验及其应用——对PPP的经验分析

通过解读一些经济变量的动态行为,提出了＂堤坝＂型确定趋势的概念和＂堤坝＂型结构突变的时间序列单位根检验。在结构突变位置未知的情况下,讨论了推断结构突变点位置的方法,给出了＂堤坝＂型结构突变单位根检验的一般步骤。最后,基于人民币和日元兑换美元的汇率数据,借助该检验为购买力平价（PPP）理论提供了有力的证据。     

On the Use of GLS Demeaning in Panel Unit Root Testing

One of the most well-known facts about unit root testing in time series is that the Dickey–Fuller (DF) test based on ordinary least squares (OLS) demeaned data suffers from low power, and that the use of generalized least squares (GLS) demeaning can lead to substantial power gains. Of course, this development has not gone unnoticed in the panel unit root literature. However, while the potential of using GLS demeaning is widely recognized, oddly enough, there are still no theoretical results available to facilitate a formal analysis of such demeaning in the panel data context. The present article can be seen as a reaction to this. The purpose is to evaluate the effect of GLS demeaning when used in conjuncture with the pooled OLS t-test for a unit root, resulting in a panel analog of the time series DF–GLS test. A key finding is that the success of GLS depend critically on the order in which the dependent variable is demeaned and first-differenced. If the variable is demeaned prior to taking first-differences, power is maximized by using GLS demeaning, whereas if the differencing is done first, then OLS demeaning is preferred. Furthermore, even if the former demeaning approach is used, such that GLS is preferred, the asymptotic distribution of the resulting test is independent of the tuning parameters that characterize the local alternative under which the demeaning performed. Hence, the demeaning can just as well be performed under the unit root null hypothesis. In this sense, GLS demeaning under the local alternative is redundant.     

平滑转换自回归模型的单位根检验问题研究

 内容提要：针对非线性模型的单位根检验中存在的问题,本文认为非线性模型的单位根检验不应该在AR模型中进行,而应该在非线性模型中进行。以LSTAR(1)模型为例,本文给出了在其中进行单位根检验的统计量及其临界值。用蒙特卡洛试验证实,本文提出的单位根检验统计量的功效明显高于DF单位根检验,只有当非平稳特征十分明显时,DF检验才能检测出其中的单位根,因此,在非线性模型中进行单位根检验是必要的。     

Panel Unit Root Tests in the Presence of Cross-Sectional Dependencies: Comparison and Implications for Modelling

Several panel unit root tests that account for cross-section dependence using a common factor structure have been proposed in the literature recently. Pesaran's (2007 Pesaran , M. H. ( 2007 ). A simple panel unit root test in the presence of cross section dependence . Journal of Applied Econometrics 22 : 265 – 312 .[Crossref], [Web of Science ®] , [Google Scholar]) cross-sectionally augmented unit root tests are designed for cases where cross-sectional dependence is due to a single factor. The Moon and Perron (2004 Moon , H. R. , Perron , B. (2004). Testing for a unit root in panels with dynamic factors. Journal of Econometrics 122:81–126.[Crossref], [Web of Science ®] , [Google Scholar]) tests which use defactored data are similar in spirit but can account for multiple common factors. The Bai and Ng (2004a Bai , J. , Ng , S. ( 2004a ). A PANIC attack on unit roots and cointegration . Econometrica 72 : 1127 – 1177 .[Crossref], [Web of Science ®] , [Google Scholar]) tests allow to determine the source of nonstationarity by testing for unit roots in the common factors and the idiosyncratic factors separately. Breitung and Das (2008 Breitung , J. , Das , S. ( 2008 ). Testing for unit roots in panels with a factor structure . Econometric Theory 24 : 88 – 108 .[Crossref], [Web of Science ®] , [Google Scholar]) and Sul (2007 Sul , D. ( 2007 ) . Panel Unit Root Tests Under Cross Section Dependence with Recursive Mean Adjustment . Mimeo : University of Auckland . [Google Scholar]) propose panel unit root tests when cross-section dependence is present possibly due to common factors, but the common factor structure is not fully exploited.

This article makes four contributions: (1) it compares the testing procedures in terms of similarities and differences in the data generation process, tests, null, and alternative hypotheses considered, (2) using Monte Carlo results it compares the small sample properties of the tests in models with up to two common factors, (3) it provides an application which illustrates the use of the tests, and (4) finally, it discusses the use of the tests in modelling in general.     

The Disappointing Properties of GLS-Based Unit Root Tests in the Presence of Structural Breaks

Abstract

It is well known that prior application of GLS detrending, as advocated by Elliot et al. [Elliot, G., Rothenberg, T., Stock, J. (1996). Efficient tests for an autoregressive unit root. Econometrica 64:813–836], can produce a significant increase in power to reject the unit root null over that obtained from a conventional OLS-based Dickey and Fuller [Dickey, D., Fuller, W. (1979). Distribution of the estimators for autoregressive time series with a unit root. J. Am. Statist. Assoc. 74:427–431] testing equation. However, this paper employs Monte Carlo simulation to demonstrate that this increase in power is not necessarily obtained when breaks occur in either level or trend. It is found that neither OLS nor GLS-based tests are robust to level or trend breaks, their size and power properties both deteriorating as the break size increases.     

Unit Roots,Level Shifts,and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards nonrejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests suffer from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This article estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per capita gross domestic product (GDP) for Organization for Economic Cooperation and Development (OECD) countries thereby permits a robust classification of countries according to the “growth shift,” “level shift,” and “linear trend” hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.     

Additive Outlier Detection and Estimation for the Logarithmic Autoregressive Conditional Duration Model

This study investigates the influences of additive outliers on financial durations. An outlier test statistic and an outlier detection procedure are proposed to detect and estimate outlier effects for the logarithmic Autoregressive Conditional Duration (Log-ACD) model. The proposed test statistic has an exact sampling distribution and performs very well, in terms of size and power, in a series of Monte Carlo simulations. Furthermore, the test statistic is robust to several alternative distribution assumptions. An empirical application shows that parameter estimates without considering outliers tend to be biased.