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.An earlier version of this paper was presented at the URCT Conference in Faro, Portugal, 2005, and at the Econometrics Seminar of the University of Zürich. We are in particular grateful to Peter Robinson and Michael Wolf for helpful comments. Moreover, we thank two anonymous referees for reports that greatly helped to improve the paper.