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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