An integration test against fractional alternatives is suggested for univariate time series+ The new test is a completely regression-based, lag augmented version of the Lagrange multiplier~LM! test by Robinson~1991, Journal of Econometrics 47, 67-84!+ Our main contributions, however, are the following+ First, we let the short memory component follow a general linear process+ Second, the innovations driving this process are martingale differences with eventual conditional heteroskedasticity that is accounted for by means of White's standard errors+ Third, we assume the number of lags to grow with the sample size, thus approximating the general linear process+ Under these assumptions, limiting normality of the test statistic is retained+ The usefulness of the asymptotic results for finite samples is established in Monte Carlo experiments+ In particular, several strategies of model selection are studied+

The inverse normal method, which is used to combine "P"-values from a series of statistical tests, requires independence of single test statistics in order to obtain asymptotic normality of the joint test statistic. The paper discusses the modification by Hartung (1999, "Biometrical Journal", Vol. 41, pp. 849-855) , which is designed to allow for a certain correlation matrix of the transformed "P"-values. First, the modified inverse normal method is shown here to be valid with more general correlation matrices. Secondly, a necessary and sufficient condition for (asymptotic) normality is provided, using the copula approach. Thirdly, applications to panels of cross-correlated time series, stationary as well as integrated, are considered. The behaviour of the modified inverse normal method is quantified by means of Monte Carlo experiments. Copyright 2006 Blackwell Publishing Ltd.

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract While the limiting null distributions of cointegration tests are invariant to a certain amount of conditional heteroskedasticity as long as global homoskedasticity conditions are fulfilled, they are certainly affected when the innovations exhibit timevarying volatility. Worse yet, distortions from single units accumulate in panels, where one must anyway pay special attention to dependence among cross-sectional units, be it time-dependent or not. To obtain a panel cointegration test robust to both global heteroskedasticity and cross-unit dependence, we start by adapting the nonlinear instruments method proposed for the Dickey-Fuller test by Chang (2002, J Econometrics 110, 261-292) to an error-correction testing framework. We show that IV-based testing of the null of no error-correction in individual equations results in asymptotic standard normality of the test statistic as long as the t-type statistics are computed with White heteroskedasticity-consistent standard errors. Remarkably, the result holds even in the presence of endogenous regressors, irrespective of the number of integrated covariates, and for any variance profile. Furthermore, a test for the null of no cointegration-in effect, a joint test against no error correction in any equation of each unit-retains the nice properties of the univariate tests. In panels with fixed cross-sectional dimension, both types of test statistics from individual units are shown to be asymptotically independent even in the presence of correlation or cointegration across units, leading to a panel test statistic robust to cross-unit dependence and unconditional heteroskedasticity. The tests perform well in panels of usual dimensions with innovations exhibiting variance breaks and a factor structure. Terms of use: Documents in

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Summary When applying Johansen's procedure for determining the cointegrating rank to systems of variables with linear deterministic trends, there are two possible tests to choose from. One test allows for a trend in the cointegration relations and the other one restricts the trend to being orthogonal to the cointegration relations. The first test is known to have reduced power relative to the second one if there is in fact no trend in the cointegration relations, whereas the second one is based on a misspecified model if the linear trend is not orthogonal to the cointegration relations. Hence, the treatment of the linear trend term is crucial for the outcome of the rank determination procedure. We compare three alternative procedures, which are applicable if there is uncertainty regarding the proper trend specification. In the first one a specific cointegrating rank is rejected if one of the two tests rejects, in the second one the trend term is decided upon by a pretest and in the third procedure only tests which allow for an unrestricted trend term are used. We provide theoretical asymptotic and small sample simulation results, which show that the first strategy is preferable in applied work.