Trend-stationary or difference-stationary?

Question

A series is Xt = 4 + 0.3\,t + \varepsilont, where \varepsilont is white noise. Is it trend-stationary or difference-stationary, and what single transformation makes it stationary?

Accepted Answer

Two flavors of nonstationarity call for two different cures: - Trend-stationary: the series is a fixed deterministic trend plus stationary noise. The cure is to detrend, subtract the estimated trend line, leaving stationary residuals. - Difference-stationary: the series has a stochastic trend (a unit root, like a random walk). The cure is to difference. Here Xt = 4 + 0.3t + \varepsilont is a deterministic straight line plus white noise, so it is trend-stationary. Subtract the trend and you recover \varepsilont, which is stationary. So the correct answer is to detrend (fit and remove 4 + 0.3t)…

Trend-stationary or difference-stationary?

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