Abstract
This paper considers testing procedures for the null hypothesis of a unit root process against the alternative of a fractional process, called a fractional unit root test. We extend the Lagrange Multiplier (LM) tests of Robinson (1994) and Tanaka (1999), which are locally best invariant and uniformly most powerful, to allow for a slope change in trend with or without a concurrent level shift under both the null and alternative hypotheses. We show that the limit distribution of the proposed LM tests is standard normal. Finite sample simulation experiments show that the tests have good size and power. As an empirical analysis, we apply the tests to the Consumer Price Indices of the G7 countries.
Highlights
Non-stationarity in economic time series is a pervasive feature
The following proposition states the limiting distribution of the Lagrange Multiplier test based on the trimmed data, which is the same as would be obtained if the break date was known in Model A2
Dolado et al (2008) [19] introduced deterministic components, the case with a structural break in trend has not been considered in the literature
Summary
Non-stationarity in economic time series is a pervasive feature. In order to carry proper inference, it is important to find the exact features that lead to this non-stationarity. Perron (1989) [1], showed that the Dickey and Fuller (1979) [2] type unit root test is biased in favor of a non-rejection of the unit root null hypothesis when the process is trend stationary with a structural change in slope. Especially that of Zivot and Andrews (1992) [5], it was common to allow for a structural break only under the alternative hypothesis, not under the null hypothesis of a unit root This is very restrictive, and can lead to misleading results. Our main contribution is to extend the LM test for a fractional unit root to allow for a structural change in a trend function under both the null and alternative hypotheses.
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