Paper #957

Title:

Testing I(1) against I(d) alternatives in the presence of deteministic components

Authors:

Juan J. Dolado, Jesús Gonzalo and Laura Mayoral

Date:

February 2005

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 I(d) processes with d € [0, 1). This is an important test in many economic applications because I(d) processess with d < 1 are mean-reverting although, when 0.5 = d < 1, like I(1) processes, they are nonstationary. We show how simple is the implementation of the FDF in these situations, and argue that it has better properties than LM tests. A simple testing strategy entailing only asymptotically normally distributed tests is also 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 OECD countries, an issue that has important consequences to discriminate between growth theories, and on which there is some controversy.

Keywords:

Deterministic components, Dickey-Fuller test, fractionally Dickey-Fuller test, fractional processes, long memory, trends, unit roots

JEL codes:

C12, C22, C40

Area of Research:

Operations Management

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