LONG MEMORY TESTING IN THE TIME DOMAIN

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+