Thanks for this interesting post. While reading it I was wondering about the potential problems with real-life data when the trend is not so obvious in the time-series plot (like in figure 1). Here, you allowed for a trend in the tests though. Is this a general advice you would give when testing for a unit-root? I noticed that for the random walk with drift it does even INcrease the p-value when not adding the trend term to the regression.
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