An Omnibus Test for Time Series Model I(d)

The fractional integrated process has been widely studied since the seminal work of Granger and Joyeus (1980). However, most of the tests for fractional integration are time-domain tests. This paper contributes to the ∗We would like to thank Jianqing Fan, N.H. Chan and Yin-Wong Cheung for helpful comments. We also thank Carrella Ernesto and Lumpkin Samuel Mcspadden for able research assistance. Corresponding author: Terence Chong, Department of Economics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong. Email: [email protected]. Webpage: http://www.cuhk.edu.hk/eco/staff/tlchong/tlchong3.htm. literature by developing a Cramér-von Mises type frequency-domain test for fractional integration. Our test is shown to have high power against a wide variety of alternatives.