Model-Selection-Based Detection of Unit Root Allowing for Various Trend-Break Types

Abstract

In the conventional hypothesis-testing approach to the detection of a unit root and a trend break, selections of the outlier type (additive or innovational) and of the break type (jump or kink) are carried out arbitrarily, because there is no generally accepted statistical technique. To overcome this problem, a model-selection approach using the modified Bayesian information criterion (MBIC) is proposed. Whether the observed time series contains a unit root and a trend break is determined as a result of model selection from among alternative models with and without unit root and trend break. The efficacy of the proposed approach is verified using comprehensive simulations.

Keywords:

• Additive outlier
• BIC
• Innovational outlier
• Model selection
• Trend break
• Unit root

Mathematics Subject Classification:

• 91B84
• 65C05

Acknowledgment

The author is grateful to the associate editor for helpful comments. Needless to say, any remaining errors belong to the author.

Notes

Note: DFT and DFF denote the Dickey–Fuller t-test and F-test for a unit root, respectively. DFTA and DFFA indicate the size-adjusted DFT and DFF test, respectively.

Note: The size of VPA is adjusted to be identical to that MBIC.

Note: The thick letter indicates the frequency count of correct selections.

Note: The thick letter indicates the frequency count of correct selections.