Keywords: Deterministic components, Dickey-Fuller test, fractionally Dickey-Fuller test, fractional processes, long memory, trends, unit roots
Abstract
This paper discusses the role of deterministic components in the DGP and in the auxiliary regression model which underlies the implementation of the Fractional Dickey- Fuller (FDF) test for I(1) against F I(d) processes with d 2 [0; 1): Invariant tests to the presence of a drift under the null of I(1) are derived. In common with the standard DF approach in the I(1) vs: I(0) framework, we also examine the consequences of including a constant and /or a linear trend in the regression model when there is a drift under the null. A simple testing strategy entailing only asymptotically normally-distributed tests is proposed. Finally, an empirical application is provided where the FDF test allowing for deterministic components is used to test for long-memory in the per capita GDP of several OCDE countries.
