Skip to content

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

An analyst models monthly log sales of a firm as ln(Y_t) = 2.50 + 0.012 t + e_t, where t = 1 for the first month and e_t is a stationary, mean-zero error. Which statement best describes this model?

The model is a log-linear trend: regressing the natural log of sales on time implies a constant proportional growth rate, so a slope of 0.012 means roughly 1.2% growth per month, not a 0.012-unit increase in levels.

  1. AA log-linear trend model in which sales grow at an approximate constant rate of 1.2% per monthCorrect
  2. BA linear trend model in which sales rise by 0.012 units each month
  3. CA random walk with drift of 0.012 per month
  4. DA quadratic trend model in which the growth rate rises over time

Explanation

Regressing the log of a series on time gives a log-linear trend. The slope 0.012 is the approximate constant proportional growth per period, i.e. 1.2% per month. The linear trend option confuses the slope in logs with a unit change in levels. A random walk with drift has stochastic, not deterministic, trend.

Did you get it right without looking?

One question tells you little. A timed set on Nonstationary Time Series shows your real accuracy, how long you take and where you lose marks.

Practise Nonstationary Time SeriesFree diagnostic mock

More Nonstationary Time Series questions