Testing for a Unit Root Against Fractional Alternatives in the Presence of a Maintained Trend

• Authors: Laura Mayoral.
• BSE Working Paper: 112321 | September 15
• Keywords: Deterministic components , Dickey-Fuller test , fractionally Dickey-Fuller test , fractional processes , long memory , trends , unit roots
• Deterministic components
• Dickey-Fuller test
• fractionally Dickey-Fuller test
• fractional processes
• long memory
• trends
• unit roots

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.