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

A series grows at a roughly constant percentage rate. An analyst estimates ln(y_t) = 2.0 + 0.03t. Which statement about the model is correct?

The series grows by about 3% each period. In a log-linear trend model the slope on time is the approximate constant continuous growth rate of the series, so a slope of 0.03 means roughly 3% growth per period.

  1. AThe series increases by about 0.03 units each period
  2. BThe series increases by about 3% each periodCorrect
  3. CThe series has a unit root with drift of 0.03
  4. DThe series is covariance stationary around a constant mean

Explanation

A log-linear trend implies a constant proportional growth rate equal to the slope, so about 3% per period. A linear trend would give constant absolute change. A deterministic trend is not a unit root, and the mean changes over time so the series is not stationary.

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