# Tests of Stationarity that are Robust to Conditional Heteroskedasticity

Besides some regularity assumptions, white noise is a solution for a GARCH process. I have simulated a GARCH process that satisfies those regularity assumptions i.e. $\alpha + \beta < 1$. However, after applying the Priestley-Subba Rao (PSR) Test of Stationarity 10000 times(fractal package), I found that it rejects the assumption of stationarity 80% of the time (at a 5% significance level). My question is therefore:

What tests of stationarity can reject the assumption of stationarity 5% of the time at a 5% significance level, specifically for GARCH processes?

set.seed(1)

library(fractal)
library(fGarch)
library(tseries)

sp <- garchSpec(model = list(alpha = 0.5, beta = 0.4))

sig = 0.05
adf.garch[i] <- adf.test(sm$garch)$p.value < sig