In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (<xref>1984</xref>, <italic>Biometrika</italic> 71, 599–607) and Chang and Park (<xref>2002</xref>, <italic>Econometric Reviews</italic> 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger,...

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)...