Testing for the General Fractional Unit Root Hypothesis in the Time Domain

Resumen

In this paper we propose a Lagrange Multiplier test as well as a family of asymptotically equivalent LS-based testing procedures which are intended to detect general forms of fractional integration at the long-run and/or the cyclical component of a time series. Our setting extends Robinson¥s (1994) approach to the time domain 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; ]. Our testing procedure can be easily implemented in practical settings and is áexible enough to account for a broad family of long- and short-memory speciÖcations, including ARMA-type and/or GARCH-type dynamics, among others. Furthermore, it has power against di§erent types of alternative hypotheses and inference is conducted under critical values drawn from a standard chi-squared distribution, independently of the long-memory parameters.