Faculty of Economics and Business Administration Publications Database

Inference on the Cointegration Rank in Fractionally Integrated Processes

Breitung, Jörg
Volume: 110
Number: 2
Pages: 167 - 185
Month: October
ISSN-Print: 0304-4076
Link External Source: Online Version
Year: 2002
Keywords: Long memory; Cointegration testing; Trace statistic; Limiting normality
Abstract: For univariate time series we suggest a new variant of efficient score tests against fractional alternatives. This test has three important merits. First, by means of simulations we observe that it is superior in terms of size and power in some situations of practical interest. Second, it is easily understood and implemented as a slight modification of the Dickey-Fuller test, although our score test has a limiting normal distribution. Third and most important, our test generalizes to multivariate cointegration tests. Thus it allows to determine the cointegration rank of fractionally integrated time series. It does so by solving a generalized eigenvalue problem of the type proposed by Johansen (1988). However, the limiting distribution of the corresponding trace statistic is chi-squared, where the degrees of freedom depend only on the cointegration rank under the null hypothesis. The usefulness of the asymptotic theory for finite samples is established in a Monte Carlo experiment.