Quant Memo
Statistics/●●●●

Trend-stationary versus difference-stationary

Two series both trend upward over time:

  • Series A: Xt=α+βt+εtX_t = \alpha + \beta t + \varepsilon_t (a deterministic line plus white noise).
  • Series B: Xt=δ+Xt1+εtX_t = \delta + X_{t-1} + \varepsilon_t (a random walk with drift).

Are either stationary? Give the correct transform to make each stationary, and explain why applying the wrong one is harmful.

Show a hint

Ask whether each series' deviation from its trend is a stable, mean-reverting quantity or a wandering, permanent one. Shocks are transient in one case and permanent in the other.

Your answer

This one is open-ended. Work it through, then check your reasoning against the full solution.

More Statistics questions