A Lagrange multiplier test for seasonal fractional integration

Abstract

This paper develops an outer product gradient (OPG) form of the Lagrange multiplier (LM) statistic for testing fractional integration at zero and seasonal frequencies in quarterly time series model. A simulation study finds that the OPG-LM test has desirable size and power properties in finite sample with the exception that this test is slightly undersized in the presence of AR(1); the power of the test is not notably affected by this size property. The OPG-LM statistic is used for testing seasonal fractional integration of quarterly Australian income and unemployment series at different frequencies and found that the former is not fractionally integrated at any frequency, and the latter is fractionally integrated at some frequencies.