Testing for Shifts in Trend with an Integrated or Stationary Noise Component

1963: The break point of the Northern Hemisphere temperature trend during the twentieth century

“…We adhere to Perron's testing methodology (Perron, 2006). First we apply the test of Perron and Yabu (2007) to ascertain the presence of a structural break. If the test favours a break, we next perform the unit root test of Kim and Perron (2006) to estimate the nature of the data generating process.…”

“…Further, we independently check our results for the break dates and the nature of the processes utilizing the different testing methodology of Zivot and Andrews (1992). The null hypothesis of the Perron-Yabu test (Perron and Yabu, 2007) is absence of a break and the alternative is a single break. The test does not require a priori specification of the break date and is valid whether the series is unit root or not.…”

Trends of U.S. Emissions of Nitrogen Oxides and Volatile Organic Compounds

“…Pretesting the data to determine if it is DS or TS is complicated by the fact that unit root tests used to determine if a series is DS or TS also depend on the whether or not there has been a shift in trend and if the timing of the shift is known or estimated. To circumvent these problems, we employ recently developed tests for shifts in trend due to Perron and Yabu (2007) that can be used without knowing if the data are DS or TS. An advantage of these tests for the pollution data is that they allow the full impact of the break to be spread over several periods.…”

Global imbalances and the intertemporal external budget constraint: A multicointegration approach

“…This pre-testing stage of the analysis is a desirable feature, as it provides an indication of whether we should then apply unit root tests with or without structural breaks depending on the outcome of the pre-test. This testing problem has recently been addressed by Perron and Yabu (2009), who de…ne a test statistic that is based on a quasi-GLS approach using an autoregression for the noise component, with a truncation to 1 when the sum of the autoregressive coe¢ cients is in some neighborhood of 1, along with a bias correction. For given break dates, one constructs the F-test (Exp W F S ) for the null hypothesis of no structural change in the deterministic components.…”

“…The …nal statistic uses the Exp functional of Andrews and Ploberger (1994). Perron and Yabu (2009) specify three di¤erent models depending on whether the structural break only a¤ects the level (Model I), the slope of the trend (Model II) or the level and the slope of the time trend (Model III). In our case, we focus on the speci…cations that allow for changes in the slope of the time series given the trending pattern that show the time series -see Figure 4.…”