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FRM Part I · FRM Exam Part I · Nonstationary Time Series

A series is generated by y_t = 2 + 0.3t + e_t, where e_t is white noise. Which statement is correct?

The series is trend-stationary. Its fluctuations around the deterministic linear trend are white noise, so subtracting the trend leaves a stationary series. Shocks are temporary, unlike a unit-root process, so detrending rather than differencing is the appropriate treatment.

  1. AThe series has a unit root, and differencing is the appropriate transformation
  2. BThe series is trend-stationary, and removing the deterministic trend gives a stationary seriesCorrect
  3. CThe series is a random walk with drift, with variance growing over time
  4. DThe series is nonstationary and cannot be made stationary by any transformation

Explanation

Deviations from the deterministic linear trend are just white noise, so the series is trend-stationary. Shocks do not persist, unlike in a unit-root process. Detrending by regression on t is the right fix; differencing would introduce a moving-average unit root (overdifferencing).

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