Size distortion of asymmetric unit root tests in the presence of level shifts

Abstract

The finite-sample size properties of momentum-threshold autoregressive (MTAR) asymmetric unit root tests are examined in the presence of level shifts under the null hypothesis. The original MTAR test using a fixed threshold is found to exhibit severe size distortion when a break in level occurs early in the sample period, leading to an increased probability of an incorrect inference of asymmetric stationarity. For later breaks the test is also shown to suffer from undersizing. In contrast, the use of consistent-threshold estimation results in a test which is relatively robust to level shifts.

Keywords:

• Unit roots
• Monte Carlo simulation
• Asymmetry
• Structural breaks

Acknowledgements

We are grateful to the editor, Professor Krutchkoff, and an anonymous referee for comments which have led to a significant improvement in the content and presentation of the paper.

Notes

See, inter alia, Banerjee et al. (1992), Perron (1989, 1990), Zivot and Andrews (1992).

In the fractional integration literature, series are non-stationary for all fractional differences d > 0.5. However, in the present context, we consider series to be stationary if d < 1.

Note 15% of the sample size represents a minimum value to ensure sufficient non-zero observations in each of the partitioned series. As the number of excluded observations is increased, the grid search procedure of consistent-threshold estimation is performed over a smaller range of values. Consequently, the properties of the Φ^*(c) test approach those of the Φ_μ test where a deterministically imposed single threshold is considered.

We are grateful to an anonymous referee for the suggestion to consider results for the smaller break size k = 0.25.

Results for the smaller sample size (T = 100) are available from the authors upon request.