Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series

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Convergence of Prices and Rates of Inflation (2006, unknown): “4 As shown in Muller (2005), a stationarity test will tend to reject the null hypothesis for highly persistent time series.”
Inflation Convergence and Divergence within the European Monetary Union (2012, background): “(1992), henceforth KPSS, and Müller (2005). It is therefore important to distinguish between convergence and stability, the former analyzed by testing the null hypothesis of unit root, the latter by testing the null of stationarity.”
The asymptotic size and power of the augmented Dickey–Fuller test for a unit root (2018, background): “In addition, Müller (2005, 2007) considered strongly autocorrelated time series and studied size and power properties of unit root tests in a local-to-unity asymptotic framework.”
A simple, robust and powerful test of the trend hypothesis (2007, background): “Speci cally, in what follows we rede ne z0 := ̂ 0 s0 and z1 := ~ 0 s1 (13) with s0 := vuut!”