Effect of a Shift in the Trend Function on Dickey–fuller Unit Root Tests

Abstract

This article analyzes the asymptotic behavior of the Dickey–Fuller unit root tests when the variable is generated under the breaking trend hypothesis. Our results show that the asymptotic behavior of these statistics allows for the rejection of the unit root hypothesis. This asymptotic finding contrasts with the results that can be found in the literature devoted to the analysis of the integration order of a variable in the presence of a structural break. However, some Monte Carlo exercises show that the argument of Perron (1989, Econometrica 57, 1361–1401) that the tests are biased in favor of nonrejection of the unit root hypothesis remains valid for sample sizes of practical interest.

Societal Violence and Collective Consciousness

“…Perron (2006Perron ( , 1989 reported that standard tests for stationarity ("unit root tests")-such as the augmented Dickey-Fuller test (Said & Dickey, 1984), Phillips-Perron test (Phillips & Perron, 1988), and others-will generally fail to reject the null hypothesis of nonstationarity when applied to a time series that is broken TS. Monte Carlo simulation experiments indicate that in this case, such tests suffer from low power and thus are biased in favor of concluding that a time series is nonstationary (Lee, Huang, & Shin,1997;Montañés & Reyes, 1998Perron, 1989Perron, , 1994. A similar bias in favor of finding nonstationarity has also been shown to apply to tests with a null hypothesis of stationarity (Kwiatkowski, Phillips, Schmidt, & Shin, 1992).…”

Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses

“…1 See also Montañés and Reyes (1998 who examined the asymptotic behavior of the Augmented Dickey-Fuller test (Dickey and Fuller, 1979;Said and Dickey, 1984) and the Phillips-Perron (Phillips and Perron, 1988) test under the crash alternative hypothesis. Leybourne et al (1998) and Leybourne and Newbold (2000) analyzed the effect of a break on a standard DF test under the unit root null hypothesis and showed that size distortions can occur, especially when the break is early in the sample.…”

Trends and random walks in macroeconomic time series: A reappraisal

“…Further, Nunes et al (1997), Montañés and Reyes (1998), Leybourne et al (1998), Lee and Strazicich (2001) and Sen (2008) found that unit root tests spuriously reject the unit root null when there is a break under the null hypothesis.…”