Comparing the small sample properties of two break Lagrange Multiplier unit root tests

In this note, we examine the size and power properties and the break date estimation accuracy of the Lee and Strazicich (LS, 2003) two break endogenous unit root test, based on two different break date selection methods: minimising the test statistic and minimising the sum of squared residuals (SSR). Our results show that the performance of both Models A and C of the LS test are superior when one uses the minimising SSR procedure.

Size and power properties of structural break unit root tests

In this article, we compare the small sample size and power properties of a newly developed endogenous structural break unit root test of Narayan and Popp (NP, 2010) with the existing two break unit root tests, namely the Lumsdaine and Papell (LP, 1997) and the Lee and Strazicich (LS, 2003) tests. In contrast to the widely used LP and LS tests, the NP test chooses the break date by maximizing the significance of the break dummy coefficient. Using Monte Carlo simulations, we show that the NP test has better size and high power, and identifies the structural breaks accurately. Power and size comparisons of the NP test with the LP and LS tests reveal that the NP test is significantly superior.

A computationally convenient unit root test with covariates, conditional heteroskedasticity and efficient detrending

When testing for a unit root in a time series, in spite of the well-known power problem of univariate tests, it is quite common to use only the information regarding the autoregressive behaviour contained in that series. In a series of influential papers, Elliott et al. (Efficient tests for an autoregressive unit root, Econometrica 64, 813–836, 1996), Hansen (Rethinking the univariate approach to unit root testing: using covariates to increase power, Econometric Theory 11, 1148–1171, 1995a) and Seo (Distribution theory for unit root tests with conditional heteroskedasticity, Journal of Econometrics 91, 113–144, 1999) showed that this practice can be rather costly and that the inclusion of the extraneous information contained in the near-integratedness of many economic variables, their heteroskedasticity and their correlation with other covariates can lead to substantial power gains. In this article, we show how these information sets can be combined into a single unit root test.

Panel versus GARCH information in unit root testing with an application to financial markets

In a search for more powerful unit root tests, some researchers have recently proposed accounting for the information contained in the GARCH of the innovations. However, while promising, tests with GARCH are difficult to implement, which has made them quite uncommon in the empirical literature. A computationally attractive alternative is to account not for GARCH but the information contained in a panel of multiple time series. The purpose of the current note is to compare the relative power achievable from these two information sources. © 2014 Elsevier B.V.

Small-sample improved seasonal unit root tests for trending and breaking series

In this article three unit root tests that allow for a break in both the seasonal mean and linear trend of the data are proposed. The tests, which can be seen as small-sample corrected versions of already known asymptotic tests, are shown to perform very well in simulations, and much better than their asymptotic counterparts.

On the choice of test for a unit root when the errors are conditionally heteroskedastic

It is well known that in the context of the classical regression model with heteroskedastic errors, while ordinary least squares (OLS) is not efficient, the weighted least squares (WLS) and quasi-maximum likelihood (QML) estimators that utilize the information contained in the heteroskedasticity are. In the context of unit root testing with conditional heteroskedasticity, while intuition suggests that a similar result should apply, the relative performance of the tests associated with the OLS, WLS and QML estimators is not well understood. In particular, while QML has been shown to be able to generate more powerful tests than OLS, not much is known regarding the relative performance of the WLS-based test. By providing an in-depth comparison of the tests, the current paper fills this gap in the literature.

A note on the use of the LLC panel unit root test

One of the single most cited studies within the field of nonstationary panel data analysis is that of LLC (Levin et al. in J Econom 98:1 - 24, 2002), in which the authors propose a test for a common unit root in the panel. Using both theoretical arguments and simulation evidence, we show that this test can be misleading unless it is based on the same bandwidth selection rule used by LLC. © Springer-Verlag 2008.

New tools for understanding the local asymptotic power of panel unit root tests

Abstract Motivated by the previously documented discrepancy between actual and predicted power, the present paper provides new tools for analyzing the local asymptotic power of panel unit root tests. These tools are appropriate in general when considering panel data with a dominant autoregressive root of the form ^ρi=1+^ciN-^κT-^τ, where i=1,...,N indexes the cross-sectional units, T is the number of time periods and ^ci is a random local-to-unity parameter. A limit theory for the sample moments of such panel data is developed and is shown to involve infinite-order series expansions in the moments of ^ci, in which existing theories can be seen as mere first-order approximations. The new theory is applied to study the asymptotic local power functions of some known test statistics for a unit root. These functions can be expressed in terms of the expansions in the moments of ^ci, and include existing local power functions as special cases. Monte Carlo evidence is provided to suggest that the new results go a long way toward bridging the gap between actual and predicted power.

Rethinking the univariate approach to panel unit root testing: using covariates to resolve the incidental trend problem

In an influential article, Hansen showed that covariate augmentation can lead to substantial power gains when compared to univariate tests. In this article, we ask if this result extends also to the panel data context? The answer turns out to be yes, which is maybe not that surprising. What is surprising, however, is the extent of the power gain, which is shown to more than outweigh the well-known power loss in the presence of incidental trends. That is, the covariates have an order effect on the neighborhood around unity for which local asymptotic power is negligible.

On the importance of the first observation in GLS detrending in unit root testing

First-differencing is generally taken to imply the loss of one observation, the first, or at least that the effect of ignoring this observation is asymptotically negligible. However, this is not always true, as in the case of generalized least squares (GLS) detrending. In order to illustrate this, the current article considers as an example the use of GLS detrended data when testing for a unit root. The results show that the treatment of the first observation is absolutely crucial for test performance, and that ignorance causes test break-down.

The asymptotic distribution of the CADF unit root test in the presence of heterogeneous AR(p) errors

The CADF test of Pesaran (J Appl Econ 22:265–312, 2007) are among the most popular univariate tests for cross-section correlated panels around. Yet, the existing asymptotic analysis of this test statistic is limited to a model in which the errors are assumed to follow a simple AR(1) structure with homogenous autoregressive coefficients. One reason for this is that the model involves an intricate identification issue, as both the serial and cross-section correlation structures of the errors are unobserved. The purpose of the current paper is to tackle this issue and in so doing extend the existing analysis to the case of AR((Formula presented.)) errors with possibly heterogeneous coefficients.

A factor analytical method to interactive effects dynamic panel models with or without unit root

In a recent study, Bai (Fixed-Effects Dynamic Panel Models, A Factor Analytical Method. Econometrica 81, 285-314, 2013a) proposes a new factor analytic (FA) method to the estimation of dynamic panel data models, which has the unique and very useful property that it is completely bias-free. However, while certainly appealing, it is restricted to fixed effects models without a unit root. In many situations of practical relevance this is a rather restrictive consideration. The purpose of the current study is therefore to extend the FA approach to cover models with multiple interactive effects and a possible unit root.

Pooled panel unit root tests and the effect of past initialization

This paper analyzes the role of initialization when testing for a unit root in panel data, an issue that has received surprisingly little attention in the literature. In fact, most studies assume that the initial value is either zero or bounded. As a response to this, the current paper considers a model in which the initialization is in the past, which is shown to have several distinctive features that makes it attractive, even in comparison to the common time series practice of making the initial value a draw from its unconditional distribution under the stationary alternative. The results have implications not only for theory, but also for applied work. In particular, and in contrast to the time series case, in panels the effect of the initialization need not be negative but can actually lead to improved test performance.