Augmented Fractional Dickey-Fuller test

For detecting the presence of a unit root in parametric time series models, the augmented Dickey-Fuller (ADF) test has become the most popular of many competing tests in the literature. The ADF test is traditionally constructed under I(1)-I(0) dichotomy, and does not  take into account the FI(d) process which is a fractionally integrated process with the differencing parameter “d” being a fractional number.

In this talk, we show that the process FI(d) has some very subtle probabilistic properties that carry out solutions to some statistical inference problems concerning the fractional integration parameter "d". In particular, we show how to exploit these properties to generalize the ADF test to the fractional case.