New innovational outlier unit root test with a break at an unknown time

Abstract

The Perron test which is based on a Dickey–Fuller test regression is a commonly employed approach to test for a unit root in the presence of a structural break of unknown timing. In the case of an innovational outlier (IO), the Perron test tends to exhibit spurious rejections in finite samples when the break occurs under the null hypothesis. In the present paper, a new Perron-type IO unit root test is developed. It is shown in Monte Carlo experiments that the new test does not over-reject the null hypothesis. Even for the case of a level and slope break for trending data, the empirical size is near its nominal level. The test distribution equals the case of a known break date. Furthermore, the test is able to identify the true break date very accurately even for small breaks. As an application serves the Nelson–Plosser data set.

Keywords:

• Unit root tests
• Structural break
• Endogenous break date estimation
• Innovational outlier models
• Spurious rejections
• Component representation

Notes

^†Cf. Schmidt and Phillips 12 and Maddala and Kim 17 for a similar problem relating to the Dickey–Fuller test.

^†It has to be noted that this test regression for M3 is qualitatively different from that for M0–M2 because it does not allow for a break under the null hypothesis. Thus, it is a joint test of the null of a unit root and no break.

^†Perron modifies the second methods insofar as he minimizes or maximizes the value (not the absolute value) of the break dummy t-statistic depending on the direction of the break in the trend function. This implies the a priori restriction of the direction of the break. Using this additional information increases the power of the test.

^‡This is not true for M3. M3 will not longer be considered explicitly, since M3 is a special case of M2.

^†GAUSS Version 3.5 http://www.aptech.com/.

^‡Because the performance of methods 1 and 2 is similar, only the results using method 2 will be displayed.