Testing for a Unit Root in Time Series With Pretest Data-Based Model Selection

Abstract

In this article we examine the impact of data-based lag-length estimation on the behavior of the augmented Dickey–Fuller (ADF) test for a unit root. We derive conditions under which the ADF test converges to the distribution tabulated by Dickey and Fuller and verify that these conditions are satisfied by several commonly employed lag-selection strategies. Simulation evidence indicates that the performance of the ADF test is considerably improved when the lag length is selected from the data. An application to inventory series illustrates that inference about a unit root can be very sensitive to the method of lag-length selection.

KEY WORDS:

• Augmented Dickey–Fuller test
• General-to-specific testing
• Information criteria
• Specific-to-general testing