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)...

Fractionally integrated time series, which have become an important modeling tool over the last two decades, are obtained by applying the fractional filter <inline-graphic>null</inline-graphic> to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response...