TESTING FOR GENERAL FRACTIONAL INTEGRATION IN THE TIME DOMAIN

We propose a family of least-squares–based testing procedures that look to detect general forms of fractional integration at the long-run and/or the cyclical component of a time series, and that are asymptotically equivalent to Lagrange multiplier tests. Our setting extends Robinson’s (1994) results to allow for short memory in a regression framework and generalizes the procedures in Agiakloglou and Newbold (1994), Tanaka (1999), and Breitung and Hassler (2002) by allowing for single or multiple fractional unit roots at any frequency in [0, <italic>π</italic>]. Our testing procedure can be easily implemented in practical settings and is flexible enough to account for a broad family of long- and short-memory specifications, including ARMA and/or GARCH-type dynamics, among others. Furthermore, these tests have power against different types of alternative hypotheses and enable inference to be conducted under critical values drawn from a standard chi-square distribution, irrespective of the long-memory parameters.