Abstract
We agree that either mistaking a stochastic trend for a deterministic trend (or vice-versa) is consequential for unit root tests and for tests of nonlinear serial dependence. In addition, we comment that similar results obtain for ordinary parameter inference in simple linear models. In particular, we note that detrending stochastically trended data with a deterministic polynomial or by applying the Hodrick–Prescott filter yields notably mis-sized hypothesis tests, even with a sample length of 200 observations. Interestingly, we further find that these size distortions persist even with stationary—albeit highly persistent—data.
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